This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the geometric properties required to define physical theories on the classified spacetime geometries. The work completed in substantiating this framework for kinematical, super-kinematical, and super-Bargmann symmetries constitutes the body of this thesis. To this end, the classification of kinematical Lie algebras in spatial dimension $D = 3$, as presented in [3, 4], is reviewed; as is the classification of spatially-isotropic homogeneous spacetimes of [5]. The derivation of geometric properties such as the non-compactness of boosts, soldering forms and vielbeins, and the space of invariant affine connections is then presented. We move on to classify the $mathcal{N}=1$ kinematical Lie superalgebras in three spatial dimensions, finding 43 isomorphism classes of Lie superalgebras. Once these algebras are determined, we classify the corresponding simply-connected homogeneous (4|4)-dimensional superspaces and show how the resulting 27 homogeneous superspaces may be related to one another via geometric limits. Finally, we turn our attention to generalised Bargmann superalgebras. In the present work, these will be the $mathcal{N}=1$ and $mathcal{N}=2$ super-extensions of the Bargmann and Newton-Hooke algebras, as well as the centrally-extended static kinematical Lie algebra, of which the former three all arise as deformations. Focussing solely on three spatial dimensions, we find $9$ isomorphism classes in the $mathcal{N}=1$ case, and we identify $22$ branches of superalgebras in the $mathcal{N}=2$ case.
{"title":"Beyond Lorentzian symmetry","authors":"Ross Grassie","doi":"10.7488/ERA/1527","DOIUrl":"https://doi.org/10.7488/ERA/1527","url":null,"abstract":"This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the geometric properties required to define physical theories on the classified spacetime geometries. The work completed in substantiating this framework for kinematical, super-kinematical, and super-Bargmann symmetries constitutes the body of this thesis. \u0000To this end, the classification of kinematical Lie algebras in spatial dimension $D = 3$, as presented in [3, 4], is reviewed; as is the classification of spatially-isotropic homogeneous spacetimes of [5]. The derivation of geometric properties such as the non-compactness of boosts, soldering forms and vielbeins, and the space of invariant affine connections is then presented. \u0000We move on to classify the $mathcal{N}=1$ kinematical Lie superalgebras in three spatial dimensions, finding 43 isomorphism classes of Lie superalgebras. Once these algebras are determined, we classify the corresponding simply-connected homogeneous (4|4)-dimensional superspaces and show how the resulting 27 homogeneous superspaces may be related to one another via geometric limits. \u0000Finally, we turn our attention to generalised Bargmann superalgebras. In the present work, these will be the $mathcal{N}=1$ and $mathcal{N}=2$ super-extensions of the Bargmann and Newton-Hooke algebras, as well as the centrally-extended static kinematical Lie algebra, of which the former three all arise as deformations. Focussing solely on three spatial dimensions, we find $9$ isomorphism classes in the $mathcal{N}=1$ case, and we identify $22$ branches of superalgebras in the $mathcal{N}=2$ case.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75427183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-09DOI: 10.21203/RS.3.RS-646944/V1
Tobias Binder
We derive differential equations from path integral based non-equilibrium quantum field theory, that cover the dynamics and spectrum of non-relativistic two-body fields for any environment. For concreteness of the two-body fields, we choose the full potential non-relativistic Quantum Electrodynamics Lagrangian in this work. After closing the correlation function hierarchy of these differential equations and performing consistency checks with previous literature under certain limits, we demonstrate the range of physics applications. This includes Cosmology such as Dark Matter in the primordial plasma, Quarkonia Physics inside a quark-gluon plasma, and Condensed and strongly Correlated Matter Physics such as Bose-Einstein condensation or Superconductivity. Since we always had to take limits or approximations of our equations in order to recover those known cases, our equations could contain new phenomena. In particular they are based on non-equilibrium Green's function that can deal with non-hermite potentials as well as dynamical formation of different extreme phases. We propose a scheme for other Lagrangian based theories or higher N-body states such as molecules to derive analogous equations.
{"title":"Path Integral based Non-equilibrium Quantum Field Theory of Non-relativistic Pairs inside an Environment","authors":"Tobias Binder","doi":"10.21203/RS.3.RS-646944/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-646944/V1","url":null,"abstract":"\u0000 We derive differential equations from path integral based non-equilibrium quantum field theory, that cover the dynamics and spectrum of non-relativistic two-body fields for any environment. For concreteness of the two-body fields, we choose the full potential non-relativistic Quantum Electrodynamics Lagrangian in this work. After closing the correlation function hierarchy of these differential equations and performing consistency checks with previous literature under certain limits, we demonstrate the range of physics applications. This includes Cosmology such as Dark Matter in the primordial plasma, Quarkonia Physics inside a quark-gluon plasma, and Condensed and strongly Correlated Matter Physics such as Bose-Einstein condensation or Superconductivity. Since we always had to take limits or approximations of our equations in order to recover those known cases, our equations could contain new phenomena. In particular they are based on non-equilibrium Green's function that can deal with non-hermite potentials as well as dynamical formation of different extreme phases. We propose a scheme for other Lagrangian based theories or higher N-body states such as molecules to derive analogous equations.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88023628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On-shell scattering amplitudes have proven to be useful tools for tackling the two-body problem in general relativity. This thesis outlines how to compute relevant classical observables that are themselves on-shell, directly from amplitudes; examples considered are the momentum impulse, total radiated momentum, and angular impulse for spinning particles. As applications we derive results relevant for black hole physics, computing in the post-Minkowskian expansion of GR, and construct a worldsheet effective action for the leading spin interactions of Kerr black holes.
{"title":"On-shell physics of black holes","authors":"Ben Maybee","doi":"10.7488/ERA/1261","DOIUrl":"https://doi.org/10.7488/ERA/1261","url":null,"abstract":"On-shell scattering amplitudes have proven to be useful tools for tackling the two-body problem in general relativity. This thesis outlines how to compute relevant classical observables that are themselves on-shell, directly from amplitudes; examples considered are the momentum impulse, total radiated momentum, and angular impulse for spinning particles. As applications we derive results relevant for black hole physics, computing in the post-Minkowskian expansion of GR, and construct a worldsheet effective action for the leading spin interactions of Kerr black holes.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75301227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-16DOI: 10.1016/j.physletb.2021.136600
Kazumi Okuyama
{"title":"Capacity of entanglement in random pure state.","authors":"Kazumi Okuyama","doi":"10.1016/j.physletb.2021.136600","DOIUrl":"https://doi.org/10.1016/j.physletb.2021.136600","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72561563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-26DOI: 10.21203/RS.3.RS-493283/V1
Latévi M. Lawson
More recently in [J. Phys. A: Math. Theor. 53, 115303 (2020)], we have introduced a set of noncommutative algebra that describes the space-time at the Planck scale. The interesting significant result we found is that the generalized uncertainty principle induced a maximal length of quantum gravity which has different physical implications to the one of generalized uncertainty principle with minimal length. The emergence of a maximal length in this theory revealed strong quantum gravitational effects at this scale and predicted the detection of gravity particles with low energies. To make evidence of these predictions, we study the dynamics of a free particle confined in an infinite square well potential in one dimension of this space. Since the effects of quantum gravity are strong in this space, we show that the energy spectrum of this system is weakly proportional to the ordinary one of quantum mechanics free of the theory of gravity. The states of this particle exhibit proprieties similar to the standard coherent states which are consequences of quantum fluctuation at this scale. Then, with the spectrum of this system at hand, we analyze the thermodynamic quantities within the canonical and microcanonical ensembles of an ideal gas made up of $N$ indistinguishable particles at the Planck scale. The results show a complete consistency between both statistical descriptions. Furthermore, a comparison with the results obtained in the context of minimal length scenarios and black hole theories indicates that the maximal length in this theory induces logarithmic corrections of deformed parameters which are consequences of a strong quantum gravitational effect.
{"title":"Thermodynamics of Ideal Gas at Planck Scale with Strong Quantum Gravity Measurement","authors":"Latévi M. Lawson","doi":"10.21203/RS.3.RS-493283/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-493283/V1","url":null,"abstract":"More recently in [J. Phys. A: Math. Theor. 53, 115303 (2020)], we have introduced a set of noncommutative algebra that describes the space-time at the Planck scale. The interesting significant result we found is that the generalized uncertainty principle induced a maximal length of quantum gravity which has different physical implications to the one of generalized uncertainty principle with minimal length. The emergence of a maximal length in this theory revealed strong quantum gravitational effects at this scale and predicted the detection of gravity particles with low energies. To make evidence of these predictions, we study the dynamics of a free particle confined in an infinite square well potential in one dimension of this space. Since the effects of quantum gravity are strong in this space, we show that the energy spectrum of this system is weakly proportional to the ordinary one of quantum mechanics free of the theory of gravity. The states of this particle exhibit proprieties similar to the standard coherent states which are consequences of quantum fluctuation at this scale. Then, with the spectrum of this system at hand, we analyze the thermodynamic quantities within the canonical and microcanonical ensembles of an ideal gas made up of $N$ indistinguishable particles at the Planck scale. The results show a complete consistency between both statistical descriptions. Furthermore, a comparison with the results obtained in the context of minimal length scenarios and black hole theories indicates that the maximal length in this theory induces logarithmic corrections of deformed parameters which are consequences of a strong quantum gravitational effect.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76227493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-02DOI: 10.1103/PhysRevD.103.116005
Matteo Buzzegoli, D. Kharzeev
The coupling between the spin of a massive Dirac fermion and the angular momentum of the medium, i.e. the gravitomagnetic moment, is shown here to be renormalized by QED interactions at finite temperature. This means that the anomalous gravitomagnetic moment (AGM) does not vanish, and implies that thermal effects can break the Einstein equivalence principle in quantum field theory, as argued previously. We also show that the AGM causes radiative corrections to the axial current of massive fermions induced by vorticity in quantum relativistic fluids, similarly to the previous findings for massless fermions. The radiative QCD effects on the AGM should significantly affect the production of polarized hadrons in heavy-ion collisions.
{"title":"Anomalous gravitomagnetic moment and nonuniversality of the axial vortical effect at finite temperature","authors":"Matteo Buzzegoli, D. Kharzeev","doi":"10.1103/PhysRevD.103.116005","DOIUrl":"https://doi.org/10.1103/PhysRevD.103.116005","url":null,"abstract":"The coupling between the spin of a massive Dirac fermion and the angular momentum of the medium, i.e. the gravitomagnetic moment, is shown here to be renormalized by QED interactions at finite temperature. This means that the anomalous gravitomagnetic moment (AGM) does not vanish, and implies that thermal effects can break the Einstein equivalence principle in quantum field theory, as argued previously. We also show that the AGM causes radiative corrections to the axial current of massive fermions induced by vorticity in quantum relativistic fluids, similarly to the previous findings for massless fermions. The radiative QCD effects on the AGM should significantly affect the production of polarized hadrons in heavy-ion collisions.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78920717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New bi-harmonic superspace formulation of 4D, $$ mathcal{N} $$ = 4 SYM theory","authors":"I. Buchbinder, E. Ivanov, V. Ivanovskiy","doi":"10.1007/JHEP04(2021)010","DOIUrl":"https://doi.org/10.1007/JHEP04(2021)010","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84705910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Kuzenko, U. Lindström, E. S. Raptakis, G. Tartaglino-Mazzucchelli
{"title":"Symmetries of $$ mathcal{N} $$ = (1, 0) supergravity backgrounds in six dimensions","authors":"S. Kuzenko, U. Lindström, E. S. Raptakis, G. Tartaglino-Mazzucchelli","doi":"10.1007/JHEP03(2021)157","DOIUrl":"https://doi.org/10.1007/JHEP03(2021)157","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87933257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-15DOI: 10.1103/PhysRevD.103.096014
B. Bajc, A. Lugo, Francesco Sannino
We investigate the high temperature fate of four dimensional gauge-Yukawa theories featuring short distance conformality of either interacting or non-interacting nature. The latter is known as complete asymptotic freedom and, as templates, we consider non-abelian gauge theories featuring either two singlet scalars coupled to gauged fermions via Yukawa interactions or two gauged scalars with(out) fermions. For theories with interacting fixed points at short distance, known as asymptotically safe, we consider two calculable examples. Exploring the landscape of safe and free theories above we discover a class of complete asymptotically free theories for which symmetry breaks at arbitrary high temperatures. In its minimal form this class is constituted by a theory with two fundamental gauged scalars each gauged under an independent group.
{"title":"Asymptotically free and safe fate of symmetry nonrestoration","authors":"B. Bajc, A. Lugo, Francesco Sannino","doi":"10.1103/PhysRevD.103.096014","DOIUrl":"https://doi.org/10.1103/PhysRevD.103.096014","url":null,"abstract":"We investigate the high temperature fate of four dimensional gauge-Yukawa theories featuring short distance conformality of either interacting or non-interacting nature. The latter is known as complete asymptotic freedom and, as templates, we consider non-abelian gauge theories featuring either two singlet scalars coupled to gauged fermions via Yukawa interactions or two gauged scalars with(out) fermions. For theories with interacting fixed points at short distance, known as asymptotically safe, we consider two calculable examples. Exploring the landscape of safe and free theories above we discover a class of complete asymptotically free theories for which symmetry breaks at arbitrary high temperatures. In its minimal form this class is constituted by a theory with two fundamental gauged scalars each gauged under an independent group.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87310666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stefano Baiguera, T. Harmark, Y. Lei, N. Wintergerst
{"title":"Symmetry structure of the interactions in near-BPS corners of $$ mathcal{N} $$ = 4 super-Yang-Mills","authors":"Stefano Baiguera, T. Harmark, Y. Lei, N. Wintergerst","doi":"10.1007/JHEP04(2021)029","DOIUrl":"https://doi.org/10.1007/JHEP04(2021)029","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83338217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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