Pub Date : 2024-07-15DOI: 10.1016/j.nuclphysb.2024.116627
This paper, as a continuation of our previous investigation [Nucl. Phys. B 1005 (2024) 116582] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective deterministic kinetic spectrum emerging from large N limit, and we extended approximate solutions using standard vertex expansion, at the leading order of the derivative expansion. Now in the following work, by introducing the non-trivial Ward identities which come from the symmetry broken of the effective kinetic action, we provide in the deep IR the explicit solution of the functional renormalization group for a model with quartic coupling by solving the Hierarchy to all orders in the local sector, which in particular imply the vanishing of the anomalous dimension. The numerical investigations confirm the first-order phase transition discovered in the vertex expansion framework, both in the active and passive schemes. Finally, we extend the discussion to hermitian matrices.
本文是我们先前研究[Nucl. Phys. B 1005 (2024) 116582]的继续,旨在研究具有淬火维格纳无序的玻璃状随机矩阵。在之前的工作中,我们基于大 N 极限出现的有效确定性动力学谱构建了重正化群,并利用标准顶点展开,在导数展开的前阶扩展了近似解。现在,在接下来的工作中,通过引入来自有效动力学作用的(U(N))×2 对称性破缺的非琐沃德同位式,我们通过求解局部扇区的所有阶次的层次结构(Hierarchy),为具有四元耦合的模型提供了函数重正化群的深红外显式解,这尤其意味着反常维度的消失。数值研究证实了在顶点扩展框架中发现的一阶相变,无论是在主动方案还是被动方案中。最后,我们将讨论扩展到了全息矩阵。
{"title":"Functional renormalization group for “p = 2” like glassy matrices in the planar approximation II. Ward identities method in the deep IR","authors":"","doi":"10.1016/j.nuclphysb.2024.116627","DOIUrl":"10.1016/j.nuclphysb.2024.116627","url":null,"abstract":"<div><p>This paper, as a continuation of our previous investigation [Nucl. Phys. B 1005 (2024) 116582] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective deterministic kinetic spectrum emerging from large N limit, and we extended approximate solutions using standard vertex expansion, at the leading order of the derivative expansion. Now in the following work, by introducing the non-trivial Ward identities which come from the <span><math><msup><mrow><mo>(</mo><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>)</mo></mrow><mrow><mo>×</mo><mn>2</mn></mrow></msup></math></span> symmetry broken of the effective kinetic action, we provide in the deep IR the explicit solution of the functional renormalization group for a model with quartic coupling by solving the Hierarchy to all orders in the local sector, which in particular imply the vanishing of the anomalous dimension. The numerical investigations confirm the first-order phase transition discovered in the vertex expansion framework, both in the active and passive schemes. Finally, we extend the discussion to hermitian matrices.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001937/pdfft?md5=e270ef0f6344bdcd74755a0795c8e4fa&pid=1-s2.0-S0550321324001937-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141728987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-15DOI: 10.1016/j.nuclphysb.2024.116630
This study investigates the application of wave functions to explore various solutions of the Klein-Gordon and Schrödinger equations within the framework of Lovelock gravity. We also present the derived Smarr formula from the topological density. The Klein-Gordon solution leads to the Wheeler-de Witt Hamiltonian and quasinormal modes, and we demonstrate the connection between the potential and the black hole temperature within the Schwarzschild limit. Additionally, we discuss different solutions of the Schrödinger equation, with one solution highlighting the influence of the Airy solution on the wave function's evolution over time.
{"title":"Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity","authors":"","doi":"10.1016/j.nuclphysb.2024.116630","DOIUrl":"10.1016/j.nuclphysb.2024.116630","url":null,"abstract":"<div><p>This study investigates the application of wave functions to explore various solutions of the Klein-Gordon and Schrödinger equations within the framework of Lovelock gravity. We also present the derived Smarr formula from the topological density. The Klein-Gordon solution leads to the Wheeler-de Witt Hamiltonian and quasinormal modes, and we demonstrate the connection between the potential and the black hole temperature within the Schwarzschild limit. Additionally, we discuss different solutions of the Schrödinger equation, with one solution highlighting the influence of the Airy solution on the wave function's evolution over time.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001962/pdfft?md5=10aee38f57fa361f2e989ff87e15cc1b&pid=1-s2.0-S0550321324001962-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141702828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-15DOI: 10.1016/j.nuclphysb.2024.116629
We investigate Klein-Gordon (KG) oscillators in a Gödel-type Som-Raychaudhuri spacetime in a mixed magnetic field (given by the vector potential , with ). The resulting KG equation takes a Schrödinger-like form (with an oscillator plus a linear plus a Coulomb-like interactions potential) that admits a solution in the form of biconfluent Heun functions/series . The usual power series expansion of which is truncated to a polynomial of order through the usual condition . However, we use the very recent recipe suggested by Mustafa [42] as an alternative parametric condition/correlation. i.e., , to facilitate conditional exact solvability of the problem. We discuss and report the effects of the mixed magnetic field as well as the effects of the Gödel-type SR-spacetime background on the KG-oscillators' spectroscopic structure.
我们研究了混合磁场(由矢量势 Aμ=(0,0,Aφ,0)给出,Aφ=B1r2/2+B2r)中哥德尔型索姆-雷乔杜里时空中的克莱因-戈登(KG)振荡器。由此产生的 KG 方程采用了类似薛定谔的形式(振荡器加线性加库仑式相互作用势),可以用双流海恩函数/序列 HB(α,β,γ,δ,z)的形式求解。通过通常的条件 γ=2(nr+1)+α,其通常的幂级数展开被截断为 nr+1=n≥1 阶的多项式。不过,我们使用了 Mustafa [42] 最近提出的方法作为替代参数条件/相关性,即 δ=-β(2nr+α+3),以促进问题的有条件精确可解性。我们讨论并报告了混合磁场以及哥德尔型 SR 时空背景对 KG 振荡器光谱结构的影响。
{"title":"KG- oscillators in Som-Raychaudhuri rotating cosmic string spacetime in a mixed magnetic field","authors":"","doi":"10.1016/j.nuclphysb.2024.116629","DOIUrl":"10.1016/j.nuclphysb.2024.116629","url":null,"abstract":"<div><p>We investigate Klein-Gordon (KG) oscillators in a Gödel-type Som-Raychaudhuri spacetime in a mixed magnetic field (given by the vector potential <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>=</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>φ</mi></mrow></msub><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span>, with <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>φ</mi></mrow></msub><mo>=</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>r</mi></math></span>). The resulting KG equation takes a Schrödinger-like form (with an oscillator plus a linear plus a Coulomb-like interactions potential) that admits a solution in the form of biconfluent Heun functions/series <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>B</mi></mrow></msub><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow></math></span>. The usual power series expansion of which is truncated to a polynomial of order <span><math><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>+</mo><mn>1</mn><mo>=</mo><mi>n</mi><mo>≥</mo><mn>1</mn></math></span> through the usual condition <span><math><mi>γ</mi><mo>=</mo><mn>2</mn><mrow><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>α</mi></math></span>. However, we use the very recent recipe suggested by Mustafa <span><span>[42]</span></span> as an alternative parametric condition/correlation. i.e., <span><math><mi>δ</mi><mo>=</mo><mo>−</mo><mi>β</mi><mrow><mo>(</mo><mn>2</mn><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>+</mo><mi>α</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></math></span>, to facilitate conditional exact solvability of the problem. We discuss and report the effects of the mixed magnetic field as well as the effects of the Gödel-type SR-spacetime background on the KG-oscillators' spectroscopic structure.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001950/pdfft?md5=03d6033cf4c7858755b24bdff9a22a7e&pid=1-s2.0-S0550321324001950-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141637988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-14DOI: 10.1016/j.nuclphysb.2024.116628
We show analytically that there exist compact stellar objects akin to neutron stars whose radius is smaller than the Schwarzschild radius defined by Arnowitt-Deser-Misner (ADM) mass. The radius of the compact object is defined by the radius where the energy density and the pressure of ordinary matter vanish, while clouds of scalar(s) can extend beyond this radius – a situation that is often encountered in modified gravity theories, like gravity and the scalar–Einstein–Gauss-Bonnet gravity. The clouds of scalar mode(s) give additional contributions to the ADM mass and as a result, the corresponding Schwarzschild radius given by the ADM mass can be larger than that of the compact object.
{"title":"Extremely small stars in scalar-tensor gravity: When stellar radius is less than Schwarzschild one","authors":"","doi":"10.1016/j.nuclphysb.2024.116628","DOIUrl":"10.1016/j.nuclphysb.2024.116628","url":null,"abstract":"<div><p>We show analytically that there exist compact stellar objects akin to neutron stars whose radius is smaller than the Schwarzschild radius defined by Arnowitt-Deser-Misner (ADM) mass. The radius of the compact object is defined by the radius where the energy density and the pressure of ordinary matter vanish, while clouds of scalar(s) can extend beyond this radius – a situation that is often encountered in modified gravity theories, like <span><math><mi>F</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> gravity and the scalar–Einstein–Gauss-Bonnet gravity. The clouds of scalar mode(s) give additional contributions to the ADM mass and as a result, the corresponding Schwarzschild radius given by the ADM mass can be larger than that of the compact object.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001949/pdfft?md5=32df75c08c210da93848a858389c373c&pid=1-s2.0-S0550321324001949-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.1016/j.nuclphysb.2024.116624
It is known that for the Heisenberg XXZ spin - chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schrödinger equation for the anharmonic oscillator.
{"title":"Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - 12 chain","authors":"","doi":"10.1016/j.nuclphysb.2024.116624","DOIUrl":"10.1016/j.nuclphysb.2024.116624","url":null,"abstract":"<div><p>It is known that for the Heisenberg XXZ spin - <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schrödinger equation for the anharmonic oscillator.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001901/pdfft?md5=372390a053136699f504a8cd5d5a4cd6&pid=1-s2.0-S0550321324001901-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141637989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.1016/j.nuclphysb.2024.116623
The left-right symmetric models (LRSM) generally include type-I and type-II induced seesaw masses as a hybrid mass for the light-active neutrinos. Assuming a particular form of Dirac-type coupling, the Majorana-type coupling present in the seesaw mass formula can be expressed in terms of low-energy neutrino oscillation observables and vacuum expectation values (vevs) of the scalar fields present in the model. The Majorana-type coupling thus admits eight different solutions by considering whether the type-I and type-II terms dominate the light neutrino mass. We study the role of all eight solutions in the lepton number violating neutrinoless double beta decay () process. In LRSM, the right-handed neutrinos, triplet scalars, and gauge bosons of the left and right sectors act as mediators of new contributions to the process. As a result, the effective mass of electron neutrino appearing in the decay width would be a function of (vev of the Higgs triplet of the right sector) along with other parameters of the model, through the masses of the new contributions. The energy scale, can be considered as the new physics scale which allows exploring physics beyond the Standard Model. Considering the present and future sensitivity of searches of , we study the role of eight different solutions of the Majorana coupling matrix. In our study, the inverted hierarchy of light neutrino masses is disfavored for all solutions keeping future sensitivity of effective mass in the picture, if the lightest mass of active neutrinos is below 0.001 eV. Also, our study shows a possibility of new physics contributions saturating the experimental bound on effective mass for in the range of 10 TeV for two particular solutions of the Majorana coupling matrix and simultaneously provides the insights about parity breaking scale.
左右对称模型(LRSM)通常包括第一类和第二类诱导跷跷板质量,作为轻活性中微子的混合质量。假设有一种特殊形式的狄拉克型耦合,跷跷板质量公式中的马约拉纳型耦合可以用低能中微子振荡观测值和模型中标量场的真空期望值(vevs)来表示。因此,通过考虑 I 型和 II 型项是否主导轻中微子质量,马约拉纳型耦合有八种不同的解决方案。我们研究了所有八种方案在违反轻子数的无中微子双β衰变(0νβ)过程中的作用。在 LRSM 中,左右部门的右手中微子、三重标量和规玻色子充当了 0νββ 过程新贡献的媒介。因此,通过新贡献的质量,衰变宽度中出现的电子中微子的有效质量将是 vR(右扇区希格斯三胞胎的脉宽)和模型其他参数的函数。能量尺度 vR 可被视为新物理学尺度,它允许探索标准模型之外的物理学。考虑到现在和未来搜索 0νββ 的灵敏度,我们研究了马约拉纳耦合矩阵的八个不同解的作用。在我们的研究中,如果有源中微子的最轻质量低于 0.001 eV,那么所有方案都不赞成轻中微子质量的倒置层次,以保持未来对有效质量的敏感性。此外,我们的研究还表明,对于马约拉纳耦合矩阵的两个特定解,新物理贡献有可能使 vR 在 10 TeV 范围内的有效质量实验约束达到饱和,并同时提供了关于奇偶性破缺尺度的见解。
{"title":"Interplay of type-I and type-II seesaw in neutrinoless double beta decay in left-right symmetric model","authors":"","doi":"10.1016/j.nuclphysb.2024.116623","DOIUrl":"10.1016/j.nuclphysb.2024.116623","url":null,"abstract":"<div><p>The left-right symmetric models (LRSM) generally include type-I and type-II induced seesaw masses as a hybrid mass for the light-active neutrinos. Assuming a particular form of Dirac-type coupling, the Majorana-type coupling present in the seesaw mass formula can be expressed in terms of low-energy neutrino oscillation observables and vacuum expectation values (vevs) of the scalar fields present in the model. The Majorana-type coupling thus admits eight different solutions by considering whether the type-I and type-II terms dominate the light neutrino mass. We study the role of all eight solutions in the lepton number violating neutrinoless double beta decay (<span><math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math></span>) process. In LRSM, the right-handed neutrinos, triplet scalars, and gauge bosons of the left and right sectors act as mediators of new contributions to the <span><math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math></span> process. As a result, the effective mass of electron neutrino appearing in the decay width would be a function of <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> (vev of the Higgs triplet of the right sector) along with other parameters of the model, through the masses of the new contributions. The energy scale, <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> can be considered as the new physics scale which allows exploring physics beyond the Standard Model. Considering the present and future sensitivity of searches of <span><math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math></span>, we study the role of eight different solutions of the Majorana coupling matrix. In our study, the inverted hierarchy of light neutrino masses is disfavored for all solutions keeping future sensitivity of effective mass in the picture, if the lightest mass of active neutrinos is below 0.001 eV. Also, our study shows a possibility of new physics contributions saturating the experimental bound on effective mass for <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> in the range of 10 TeV for two particular solutions of the Majorana coupling matrix and simultaneously provides the insights about parity breaking scale.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001895/pdfft?md5=fa628352c9f31036801eeaf1d1b6dd5c&pid=1-s2.0-S0550321324001895-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141637088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.1016/j.nuclphysb.2024.116622
Recent work has highlighted the importance of crossed products in correctly elucidating the operator algebraic approach to quantum field theories. In the gravitational context, the crossed product simultaneously promotes von Neumann algebras associated with subregions in diffeomorphism covariant quantum field theories from type III to type II, and provides the necessary ingredients to gravitationally dress operators, thereby enforcing the constraints of the theory. In this note we enhance the crossed product construction to the context of general gauge theories with arbitrary combinations of internal and spacetime local symmetries. This is done by leveraging the correspondence between the crossed product and the extended phase space. We then undertake a detailed study of constraint quantization from the perspective of a generic crossed product algebra. We study and compare four distinct approaches to constraint quantization from this point of view: refined algebraic quantization, BRST quantization, path integral quantization, and the commutation theorem for crossed products. Far from simply reproducing existing analyses, the operator algebraic viewpoint sheds new light on old problems by reformulating the dressing of operators in terms of conditional expectations and other closely related projection maps. We conclude by applying our approach to the constraint quantization of three distinct gauge theories including a discussion of gravity on null hypersurfaces.
最近的研究突出了交叉积在正确阐明量子场论的算子代数方法方面的重要性。在引力背景下,交叉积同时将与衍射协变量子场论中子区域相关的冯-诺依曼代数从 III 型提升到 II 型,并提供了引力修饰算子的必要成分,从而加强了理论的约束。在本论文中,我们将交叉乘积构造增强到具有任意内部和时空局部对称性组合的一般量规理论中。这是通过利用交叉积和扩展相空间之间的对应关系来实现的。然后,我们从一般交叉积代数的角度对约束量子化进行了详细研究。从这个角度出发,我们研究并比较了四种不同的约束量化方法:精炼代数量化、BRST 量化、路径积分量化和交叉积的换向定理。算子代数观点绝非简单地复制现有的分析,而是通过用条件期望和其他密切相关的投影图来重新表述算子的敷料,从而为老问题带来了新的启示。最后,我们将把我们的方法应用于三种不同规规理论的约束量子化,包括讨论空超曲面上的引力。
{"title":"Crossed products, conditional expectations and constraint quantization","authors":"","doi":"10.1016/j.nuclphysb.2024.116622","DOIUrl":"10.1016/j.nuclphysb.2024.116622","url":null,"abstract":"<div><p>Recent work has highlighted the importance of crossed products in correctly elucidating the operator algebraic approach to quantum field theories. In the gravitational context, the crossed product simultaneously promotes von Neumann algebras associated with subregions in diffeomorphism covariant quantum field theories from type III to type II, and provides the necessary ingredients to gravitationally dress operators, thereby enforcing the constraints of the theory. In this note we enhance the crossed product construction to the context of general gauge theories with arbitrary combinations of internal and spacetime local symmetries. This is done by leveraging the correspondence between the crossed product and the extended phase space. We then undertake a detailed study of constraint quantization from the perspective of a generic crossed product algebra. We study and compare four distinct approaches to constraint quantization from this point of view: refined algebraic quantization, BRST quantization, path integral quantization, and the commutation theorem for crossed products. Far from simply reproducing existing analyses, the operator algebraic viewpoint sheds new light on old problems by reformulating the dressing of operators in terms of conditional expectations and other closely related projection maps. We conclude by applying our approach to the constraint quantization of three distinct gauge theories including a discussion of gravity on null hypersurfaces.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001883/pdfft?md5=d65d1d8761875719b14fb2ca269de468&pid=1-s2.0-S0550321324001883-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141630730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.1016/j.nuclphysb.2024.116625
A model of N 4-component massless fermions in a quartic self-interaction based on ref. [19] is investigated in the presence of chemical potential and temperature via optimized perturbation theory that accesses finite-N contributions. We use the generating functional approach to calculate the corrections to the effective potential of the model. The model introduces an auxiliary pseudo-vector field with a nontrivial minimum and is influenced by temperature (T) and chemical potential (μ). These thermodynamic quantities are introduced through Matsubara formalism. Thereby, the integrals are modified, and via the principle of minimum sensitivity, we obtain the gap equations of the model. The correspondent finite-N solutions of these equations define the vacuum states of the model associated with the background pseudo-vector field. In particular, one focuses on its temporal component that acts as an effective chiral chemical potential. We discuss the solutions of the four cases in which , , and , where the effective potential is so obtained as a function of the background vector field, the chemical potential, and the temperature. The model shows the finite-N corrections generate first-order phase transitions on the self-interacting fermions for the case and the persistence of a second-order phase transition for .
基于参考文献[19]的 N 个 4 分量无质量费米子的四元自相互作用模型,通过优化的扰动理论研究了存在化学势和温度时的有限 N 贡献。[19]的模型,通过优化微扰理论研究了存在化学势和温度时的有限 N 贡献。我们使用生成函数法计算模型有效势的修正。该模型引入了一个辅助伪矢量场,该场有一个非rivial的最小值,并受温度(T)和化学势(μ)的影响。这些热力学量是通过松原形式主义引入的。因此,我们修改了积分,并通过最小灵敏度原理得到了模型的间隙方程。这些方程的相应有限 N 解定义了模型与背景伪向量场相关的真空状态。我们尤其关注其作为有效手性化学势的时间分量。我们讨论了 (T=0,μ=0)、(T≠0,μ≠0)、(T≠0,μ=0) 和 (T=0,μ≠0) 四种情况下的解,其中有效化学势是作为背景矢量场、化学势和温度的函数得到的。模型显示,在 N=1 的情况下,有限 N 修正会在自相互作用费米子上产生一阶相变,而在 N≥2 的情况下,二阶相变会持续存在。
{"title":"First-order phase-transition on dynamical Lorentz symmetry breaking system","authors":"","doi":"10.1016/j.nuclphysb.2024.116625","DOIUrl":"10.1016/j.nuclphysb.2024.116625","url":null,"abstract":"<div><p>A model of <em>N</em> 4-component massless fermions in a quartic self-interaction based on ref. <span><span>[19]</span></span> is investigated in the presence of chemical potential and temperature via optimized perturbation theory that accesses finite-N contributions. We use the generating functional approach to calculate the corrections to the effective potential of the model. The model introduces an auxiliary pseudo-vector field with a nontrivial minimum and is influenced by temperature (<em>T</em>) and chemical potential (<em>μ</em>). These thermodynamic quantities are introduced through Matsubara formalism. Thereby, the integrals are modified, and via the principle of minimum sensitivity, we obtain the gap equations of the model. The correspondent finite-N solutions of these equations define the vacuum states of the model associated with the background pseudo-vector field. In particular, one focuses on its temporal component that acts as an effective chiral chemical potential. We discuss the solutions of the four cases in which <span><math><mo>(</mo><mi>T</mi><mo>=</mo><mn>0</mn><mo>,</mo><mi>μ</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></span>, <span><math><mo>(</mo><mi>T</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mi>μ</mi><mo>≠</mo><mn>0</mn><mo>)</mo></math></span>, <span><math><mo>(</mo><mi>T</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mi>μ</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>T</mi><mo>=</mo><mn>0</mn><mo>,</mo><mi>μ</mi><mo>≠</mo><mn>0</mn><mo>)</mo></math></span>, where the effective potential is so obtained as a function of the background vector field, the chemical potential, and the temperature. The model shows the finite-N corrections generate first-order phase transitions on the self-interacting fermions for the case <span><math><mi>N</mi><mo>=</mo><mn>1</mn></math></span> and the persistence of a second-order phase transition for <span><math><mi>N</mi><mo>≥</mo><mn>2</mn></math></span>.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001913/pdfft?md5=6a15199cbd6d7a49b9f0f84175d479a3&pid=1-s2.0-S0550321324001913-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141728988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.1016/j.nuclphysb.2024.116626
We have investigated a weakly q-deformed algebra, which leads to non-Hermitian operators. It has been explicitly shown that the harmonic oscillator Hamiltonian is quasi-Hermitian, and that the corresponding physical Hilbert-space metric Θ differs from that obtained in Ref. [1], by hermitizing the position operator. The reality of the Hamiltonian eigenvalues has been illustrated by analytically computing the first order correction to the energy spectrum of the harmonic oscillator (HO). Furthermore, we have shown that this q-deformation leads to a GUP with minimal uncertainties in both position and momentum measurements. Moreover, the physical implications of this q-deformation, have been investigated by studying the thermostatistics of a system of HOs and an ideal gas. For both systems, we computed the partition function, and then we derived some thermodynamic functions. In addition, for the ideal gas, a modified equation of state and a generalized Mayer's equation, consistent with the real behavior of gases, have been established. The obtained results show that the impact of this model would be significant at high temperatures. However, unlike earlier research, we observe that this q-deformation induced the similar corrections regardless of the system under study.
{"title":"Weakly q-deformed Heisenberg algebra and non-Hermitian Hamiltonians: Application in statistical physics","authors":"","doi":"10.1016/j.nuclphysb.2024.116626","DOIUrl":"10.1016/j.nuclphysb.2024.116626","url":null,"abstract":"<div><p>We have investigated a weakly <em>q</em>-deformed algebra, which leads to non-Hermitian operators. It has been explicitly shown that the harmonic oscillator Hamiltonian is quasi-Hermitian, and that the corresponding physical Hilbert-space metric Θ differs from that obtained in Ref. <span><span>[1]</span></span>, by hermitizing the position operator. The reality of the Hamiltonian eigenvalues has been illustrated by analytically computing the first order correction to the energy spectrum of the harmonic oscillator (HO). Furthermore, we have shown that this <em>q</em>-deformation leads to a GUP with minimal uncertainties in both position and momentum measurements. Moreover, the physical implications of this <em>q</em>-deformation, have been investigated by studying the thermostatistics of a system of HOs and an ideal gas. For both systems, we computed the partition function, and then we derived some thermodynamic functions. In addition, for the ideal gas, a modified equation of state and a generalized Mayer's equation, consistent with the real behavior of gases, have been established. The obtained results show that the impact of this model would be significant at high temperatures. However, unlike earlier research, we observe that this <em>q</em>-deformation induced the similar corrections regardless of the system under study.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001925/pdfft?md5=b9ff8bb859da20c13bc55e6318936deb&pid=1-s2.0-S0550321324001925-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141697231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-09DOI: 10.1016/j.nuclphysb.2024.116621
The wormhole solution in dRGT massive gravity is examined in this paper in the background of non-commutative geometry. In order to derive the wormhole model, along with the zero tidal force, we assume that the matter distribution is given by the Gaussian and Lorentzian distributions. The shape function in both models involves the massive gravity parameters and . But the spacetime loses its asymptotic flatness due to the action of the massive gravity parameter. It is noticed that the asymptotic flatness is affected by the repulsive effect induced in the massive gravitons that push the spacetime geometry very strongly. We observed that each model violates the null energy criteria, indicating the presence of exotic matter which is necessary to sustain the wormholes. The exotic matter is measured using the volume integral quantifier. Moreover, it is discovered that the model is stable under the hydrostatic equilibrium condition by utilizing the TOV equation. Finally, our research encompassed an exploration of the repulsive influence exerted by gravity. Our findings demonstrated that the presence of repulsive gravity results in a negative deflection angle for photons following null geodesics. Remarkably, we consistently observed negative values for the deflection angle across all values of in the two scenarios examined. This consistent negativity unequivocally signifies the manifestation of the repulsive gravity effect.
{"title":"Noncommutative wormhole in de Rham-Gabadadze-Tolley like massive gravity","authors":"","doi":"10.1016/j.nuclphysb.2024.116621","DOIUrl":"10.1016/j.nuclphysb.2024.116621","url":null,"abstract":"<div><p>The wormhole solution in dRGT massive gravity is examined in this paper in the background of non-commutative geometry. In order to derive the wormhole model, along with the zero tidal force, we assume that the matter distribution is given by the Gaussian and Lorentzian distributions. The shape function in both models involves the massive gravity parameters <span><math><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. But the spacetime loses its asymptotic flatness due to the action of the massive gravity parameter. It is noticed that the asymptotic flatness is affected by the repulsive effect induced in the massive gravitons that push the spacetime geometry very strongly. We observed that each model violates the null energy criteria, indicating the presence of exotic matter which is necessary to sustain the wormholes. The exotic matter is measured using the volume integral quantifier. Moreover, it is discovered that the model is stable under the hydrostatic equilibrium condition by utilizing the TOV equation. Finally, our research encompassed an exploration of the repulsive influence exerted by gravity. Our findings demonstrated that the presence of repulsive gravity results in a negative deflection angle for photons following null geodesics. Remarkably, we consistently observed negative values for the deflection angle across all values of <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> in the two scenarios examined. This consistent negativity unequivocally signifies the manifestation of the repulsive gravity effect.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001871/pdfft?md5=e6440babf73e2e4f4e5aeeec21d2bf74&pid=1-s2.0-S0550321324001871-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141637053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}