Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00063-1
Yuji Hirota, Noriaki Ikeda
A reduction theorem for Poisson manifolds with Hamiltonian Lie algebroids is presented. The notion of compatibility of a momentum section is introduced to the category of Hamiltonian Lie algebroids over Poisson manifolds. It is shown that a compatible momentum section is a Lie algebra homomorphism, and then the quotient space of the zero level set of a compatible momentum section proves to be a Poisson manifold.
{"title":"Reduction Of Poisson Manifolds With Hamiltonian Lie Algebroids","authors":"Yuji Hirota, Noriaki Ikeda","doi":"10.1016/S0034-4877(25)00063-1","DOIUrl":"10.1016/S0034-4877(25)00063-1","url":null,"abstract":"<div><div>A reduction theorem for Poisson manifolds with Hamiltonian Lie algebroids is presented. The notion of compatibility of a momentum section is introduced to the category of Hamiltonian Lie algebroids over Poisson manifolds. It is shown that a compatible momentum section is a Lie algebra homomorphism, and then the quotient space of the zero level set of a compatible momentum section proves to be a Poisson manifold.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 201-212"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00067-9
Komal Singla
In this paper, the exact solutions of space-time fractional Caudrey-Dodd-Gibbon equation are investigated by implementing the symmetry approach and power series method. The reported solutions are very interesting due to their novelty and significance in the field of fractional calculus. The graphical behaviour of the solutions is also interpreted in the present study.
{"title":"On Investigation Of Solutions For Caudrey-Dodd-Gibbon Equation With Space-Time Fractional Derivatives","authors":"Komal Singla","doi":"10.1016/S0034-4877(25)00067-9","DOIUrl":"10.1016/S0034-4877(25)00067-9","url":null,"abstract":"<div><div>In this paper, the exact solutions of space-time fractional Caudrey-Dodd-Gibbon equation are investigated by implementing the symmetry approach and power series method. The reported solutions are very interesting due to their novelty and significance in the field of fractional calculus. The graphical behaviour of the solutions is also interpreted in the present study.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 265-273"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00066-7
Hiroshi Inoue
In this paper we shall study *-automorphisms of an unbounded observable algebra called T†-algebras. The first purpose is to investigate when a *-automorphism α of a T† -algebra on a dense subspace D in a Hilbert space H is represented as α = Tg ∘ IU ∘ Sγ by a unitary transform IU, a similar transform Sγ and a translation Tg of . The second purpose is to investigate when α is a unitary transform, namely α = IU.
{"title":"On *-Automorphisms Of Unbounded Observable Algebras","authors":"Hiroshi Inoue","doi":"10.1016/S0034-4877(25)00066-7","DOIUrl":"10.1016/S0034-4877(25)00066-7","url":null,"abstract":"<div><div>In this paper we shall study *-automorphisms of an unbounded observable algebra called <em>T</em><sup>†</sup>-algebras. The first purpose is to investigate when a *-automorphism <em>α</em> of a T<sup>†</sup> -algebra \u0000\t\t\t\t<span><math><mi>A</mi></math></span> on a dense subspace <em>D</em> in a Hilbert space <em>H</em> is represented as <em>α = T<sub>g</sub> ∘ I<sub>U</sub> ∘ S<sub>γ</sub></em> by a unitary transform <em>I<sub>U</sub></em>, a similar transform <em>S<sub>γ</sub></em> and a translation <em>T<sub>g</sub></em> of \u0000\t\t\t\t<span><math><mi>A</mi></math></span>. The second purpose is to investigate when <em>α</em> is a unitary transform, namely <em>α = I<sub>U</sub></em>.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 255-263"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00064-3
Giuseppe Dattoli, Subuhi Khan, Ujair Ahmad
A symbolic method of umbral nature is employed to evaluate a family of infinite integrals containing combinations of various functions, including exponentials, logarithms, and products of Bessel functions of different types. The methods developed in this article are naturally suited for studying integrals, including Macdonald Bessel functions, and offer a particularly useful tool for working out the relevant details with minimal computational efforts.
{"title":"Evaluation Of Integrals Of Bessel Functions With Umbral Methods","authors":"Giuseppe Dattoli, Subuhi Khan, Ujair Ahmad","doi":"10.1016/S0034-4877(25)00064-3","DOIUrl":"10.1016/S0034-4877(25)00064-3","url":null,"abstract":"<div><div>A symbolic method of umbral nature is employed to evaluate a family of infinite integrals containing combinations of various functions, including exponentials, logarithms, and products of Bessel functions of different types. The methods developed in this article are naturally suited for studying integrals, including Macdonald Bessel functions, and offer a particularly useful tool for working out the relevant details with minimal computational efforts.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 213-226"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00060-6
C. Quesne
It is shown that the rich algebraic structure of the standard d-dimensional Coulomb problem can be extended to its Dunkl counterpart. Replacing standard derivatives by Dunkl ones in the so(d + 1,2) dynamical algebra generators of the former gives rise to a deformed algebra with similar commutation relations, except that the metric tensor becomes dependent on the reflection operators and that there are some additional commutation or anticommutation relations involving the latter. It is then shown that from some of the dynamical algebra generators it is straightforward to derive the integrals of motion of the Dunkl–Coulomb problem in Sturm representation. Finally, from the latter, the components of a deformed Laplace–Runge–Lenz vector are built. Together with the Dunkl angular momentum components, such operators insure the superintegrability of the Dunkl–Coulomb problem in Schrödinger representation.
{"title":"Dynamical And Invariance Algebras Of The D-Dimensional Dunkl-Coulomb Problem","authors":"C. Quesne","doi":"10.1016/S0034-4877(25)00060-6","DOIUrl":"10.1016/S0034-4877(25)00060-6","url":null,"abstract":"<div><div>It is shown that the rich algebraic structure of the standard <em>d</em>-dimensional Coulomb problem can be extended to its Dunkl counterpart. Replacing standard derivatives by Dunkl ones in the so(<em>d +</em> 1,2) dynamical algebra generators of the former gives rise to a deformed algebra with similar commutation relations, except that the metric tensor becomes dependent on the reflection operators and that there are some additional commutation or anticommutation relations involving the latter. It is then shown that from some of the dynamical algebra generators it is straightforward to derive the integrals of motion of the Dunkl–Coulomb problem in Sturm representation. Finally, from the latter, the components of a deformed Laplace–Runge–Lenz vector are built. Together with the Dunkl angular momentum components, such operators insure the superintegrability of the Dunkl–Coulomb problem in Schrödinger representation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 147-158"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00062-X
Roman Urban
Let K be an algebraic number field. Let α be a Vladimirov type operator on the free module of rank d over a ring of finite adeles . We consider the Schrödinger operator HV(t) =Dα + V(t) with a nonnegative, bounded, time-dependent potential V(t). We prove a version of the Feynman–Kac formula for the evolution family generated by the Schrödinger operator HV(t) and show that can be expressed in the form of the Dyson-type series.
{"title":"Feynman-Kac Integral And Dyson-Type Series Representations For The Schrödinger Equation On Finite Adeles","authors":"Roman Urban","doi":"10.1016/S0034-4877(25)00062-X","DOIUrl":"10.1016/S0034-4877(25)00062-X","url":null,"abstract":"<div><div>Let K be an algebraic number field. Let <strong><sup><em>α</em></sup></strong> be a Vladimirov type operator on the free module of rank d over a ring of finite adeles \u0000\t\t\t\t<span><math><msub><mi>A</mi><mi>K</mi></msub></math></span>. We consider the Schrödinger operator <em>H<sub>V</sub></em>(<em>t</em>) <em>=</em> <strong>D</strong><sup><em>α</em></sup> + V(<em>t</em>) with a nonnegative, bounded, time-dependent potential V(<em>t</em>). We prove a version of the Feynman–Kac formula for the evolution family \u0000\t\t\t\t<span><math><msubsup><mi>T</mi><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow><mi>V</mi></msubsup></math></span> generated by the Schrödinger operator <em>H<sub>V</sub></em>(<em>t</em>) and show that \u0000\t\t\t\t<span><math><msubsup><mi>T</mi><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow><mi>V</mi></msubsup></math></span> can be expressed in the form of the Dyson-type series.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 189-199"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/S0034-4877(25)00065-5
Piotr Stachura
This article presents a differential groupoid with “coaction” of the groupoid underlying the quantum Euclidean group (i.e. its C*-algebra is the C*-algebra of this quantum group). The dual of the Lie algebroid is a Poisson manifold that can be identified with the space of oriented lines in Euclidean space equipped with a Poisson action of the Poisson–Lie Euclidean group.
{"title":"A Quantum Space Of Euclidean Lines","authors":"Piotr Stachura","doi":"10.1016/S0034-4877(25)00065-5","DOIUrl":"10.1016/S0034-4877(25)00065-5","url":null,"abstract":"<div><div>This article presents a differential groupoid with “coaction” of the groupoid underlying the quantum Euclidean group (i.e. its C*-algebra is the C*-algebra of this quantum group). The dual of the Lie algebroid is a Poisson manifold that can be identified with the space of oriented lines in Euclidean space equipped with a Poisson action of the Poisson–Lie Euclidean group.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 2","pages":"Pages 227-254"},"PeriodicalIF":1.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-01DOI: 10.1016/S0034-4877(25)00053-9
Jan Derezinski , Barteomiej Sikorski
We review properties of Bessel potentials, that is, inverse Fourier transforms of (regularizations of) on a pseudo-Euclidean space with signature (q, d-q). We are mostly interested in the Lorentzian signature (1,d- 1), and the case = 2, related to the Klein-Gordon equation We analyze properties of various “propagators”, which play an important role in quantum field theory, such as the retarded/advanced propagators or Feynman/anti-Feynman propagators. We consistently use hypergeometric functions instead of Bessel functions, which makes most formulae much more transparent. We pay attention to distributional properties of various Bessel potentials. We include in our analysis the “tachyonic case”, corresponding to the “wrong” sign in the Klein-Gordon equation.
{"title":"Bessel Potentials and Green Functions on Pseudo-Euclidean Spaces","authors":"Jan Derezinski , Barteomiej Sikorski","doi":"10.1016/S0034-4877(25)00053-9","DOIUrl":"10.1016/S0034-4877(25)00053-9","url":null,"abstract":"<div><div>We review properties of Bessel potentials, that is, inverse Fourier transforms of (regularizations of) \u0000\t\t\t\t<span><math><msup><mrow><mo>(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><msup><mi>p</mi><mn>2</mn></msup><mo>)</mo></mrow><mrow><mo>−</mo><mfrac><mi>μ</mi><mn>2</mn></mfrac></mrow></msup></math></span> on a pseudo-Euclidean space with signature <em>(q, d-q</em>). We are mostly interested in the Lorentzian signature <em>(1,d- 1)</em>, and the case = 2, related to the Klein-Gordon equation \u0000\t\t\t\t<span><math><mo>(</mo><mo>−</mo><mi>◻</mi><mo>+</mo><msup><mi>m</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo><mi>f</mi><mo>=</mo><mn>0</mn></math></span> We analyze properties of various “propagators”, which play an important role in quantum field theory, such as the retarded/advanced propagators or Feynman/anti-Feynman propagators. We consistently use hypergeometric functions instead of Bessel functions, which makes most formulae much more transparent. We pay attention to distributional properties of various Bessel potentials. We include in our analysis the “tachyonic case”, corresponding to the “wrong” sign in the Klein-Gordon equation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 1","pages":"Pages 19-54"},"PeriodicalIF":1.2,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-01DOI: 10.1016/S0034-4877(25)00057-6
Pavel Exner, Jan Pekar
We analyze the spectrum of the hexagonal lattice graph with a vertex coupling which manifestly violates the time reversal invariance and at high energies it exhibits a nontrivial transport at odd-degree vertices; a comparison is made to the case when the edges are effectively decoupled at such vertices. We also show that the spectral character does not change if the equilateral elementary cell of the lattice is dilated to have three different edge lengths, except that flat bands are absent if those are incommensurate.
{"title":"Spectral Properties of Hexagonal Lattices with The -R Coupling","authors":"Pavel Exner, Jan Pekar","doi":"10.1016/S0034-4877(25)00057-6","DOIUrl":"10.1016/S0034-4877(25)00057-6","url":null,"abstract":"<div><div>We analyze the spectrum of the hexagonal lattice graph with a vertex coupling which manifestly violates the time reversal invariance and at high energies it exhibits a nontrivial transport at odd-degree vertices; a comparison is made to the case when the edges are effectively decoupled at such vertices. We also show that the spectral character does not change if the equilateral elementary cell of the lattice is dilated to have three different edge lengths, except that flat bands are absent if those are incommensurate.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 1","pages":"Pages 101-114"},"PeriodicalIF":1.2,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145370999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-01DOI: 10.1016/S0034-4877(25)00055-2
Jiale Meng, Guanghui Jin
In this paper, we study the generalized Maxwell-Chern-Simons-Higgs equation. We derive its one-dimensional formulation and establish the local well-posedness of the Cauchy problem under the Lorenz gauge condition. Building on the ideas from [9, 10], we introduce suitable modifications to prove our main result.
{"title":"Local Well-Posedness of Generalized Maxwell-Chern-Simons-Higgs Equation in ℝ1+1","authors":"Jiale Meng, Guanghui Jin","doi":"10.1016/S0034-4877(25)00055-2","DOIUrl":"10.1016/S0034-4877(25)00055-2","url":null,"abstract":"<div><div>In this paper, we study the generalized Maxwell-Chern-Simons-Higgs equation. We derive its one-dimensional formulation and establish the local well-posedness of the Cauchy problem under the Lorenz gauge condition. Building on the ideas from [<span><span>9</span></span>, <span><span>10</span></span>], we introduce suitable modifications to prove our main result.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"96 1","pages":"Pages 75-83"},"PeriodicalIF":1.2,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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