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Affine manifolds: The differential geometry of the multi-dimensionally consistent TED equation 仿射流形：多维一致 TED 方程的微分几何学
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-14 DOI: 10.1016/j.geomphys.2024.105366
W.K. Schief , U. Hertrich-Jeromin , B.G. Konopelchenko
{"title":"Affine manifolds: The differential geometry of the multi-dimensionally consistent TED equation","authors":"W.K. Schief ,&nbsp;U. Hertrich-Jeromin ,&nbsp;B.G. Konopelchenko","doi":"10.1016/j.geomphys.2024.105366","DOIUrl":"10.1016/j.geomphys.2024.105366","url":null,"abstract":"<div><div>It is shown that a canonical geometric setting of the integrable TED equation is a Kählerian tangent bundle of an affine manifold. The remarkable multi-dimensional consistency of this 4+4-dimensional dispersionless partial differential equation arises naturally in this context. In a particular 4-dimensional reduction, the affine manifolds turn out to be self-dual Einstein spaces of neutral signature governed by Plebański's first heavenly equation. In another reduction, the affine manifolds are Hessian, governed by compatible general heavenly equations. The Legendre invariance of the latter gives rise to a (dual) Hessian structure. Foliations of affine manifolds in terms of self-dual Einstein spaces are also shown to arise in connection with a natural 5-dimensional reduction.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105366"},"PeriodicalIF":1.6,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit evaluation of the Stokes matrices for certain quantum confluent hypergeometric equations
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-14 DOI: 10.1016/j.geomphys.2024.105364
Jinghong Lin , Xiaomeng Xu
{"title":"Explicit evaluation of the Stokes matrices for certain quantum confluent hypergeometric equations","authors":"Jinghong Lin ,&nbsp;Xiaomeng Xu","doi":"10.1016/j.geomphys.2024.105364","DOIUrl":"10.1016/j.geomphys.2024.105364","url":null,"abstract":"<div><div>In this paper, we compute the Stokes matrices of a special quantum confluent hypergeometric system with Poincaré rank one. The interest in the Stokes phenomenon of such a system arises from representation theory and the theory of isomonodromy deformation.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105364"},"PeriodicalIF":1.6,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143092483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conformal and contact kinetic dynamics and their geometrization
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-14 DOI: 10.1016/j.geomphys.2024.105369
Oğul Esen , Ayten Gezici , Miroslav Grmela , Hasan Gümral , Michal Pavelka , Serkan Sütlü
{"title":"Conformal and contact kinetic dynamics and their geometrization","authors":"Oğul Esen ,&nbsp;Ayten Gezici ,&nbsp;Miroslav Grmela ,&nbsp;Hasan Gümral ,&nbsp;Michal Pavelka ,&nbsp;Serkan Sütlü","doi":"10.1016/j.geomphys.2024.105369","DOIUrl":"10.1016/j.geomphys.2024.105369","url":null,"abstract":"<div><div>We propose a conformal generalization of the reversible Vlasov equation of kinetic plasma dynamics, called conformal kinetic theory. In order to arrive at this formalism, we start with the conformal Hamiltonian dynamics of particles and lift it to the dynamical formulation of the associated kinetic theory. The resulting theory represents a simple example of a geometric pathway from dissipative particle motion to dissipative kinetic motion. We also derive the kinetic equations of a continuum of particles governed by the contact Hamiltonian dynamics, which may be interpreted in the context of relativistic mechanics. Once again we start with the contact Hamiltonian dynamics and lift it to a kinetic theory, called contact kinetic dynamics. Finally, we project the contact kinetic theory to conformal kinetic theory so that they form a geometric hierarchy.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"209 ","pages":"Article 105369"},"PeriodicalIF":1.6,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Klein-Gordon oscillators and Bergman spaces 克莱因-戈登振荡器和伯格曼空间
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-14 DOI: 10.1016/j.geomphys.2024.105368
Alexander D. Popov
{"title":"Klein-Gordon oscillators and Bergman spaces","authors":"Alexander D. Popov","doi":"10.1016/j.geomphys.2024.105368","DOIUrl":"10.1016/j.geomphys.2024.105368","url":null,"abstract":"<div><div>We consider classical and quantum dynamics of relativistic oscillator in Minkowski space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>. It is shown that for a non-zero frequency parameter <em>ω</em> the covariant phase space of the classical Klein-Gordon oscillator is a homogeneous Kähler-Einstein manifold <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>=</mo><mrow><mi>Ad</mi></mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>7</mn></mrow></msub><mo>/</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>=</mo><mi>U</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>. In the limit <span><math><mi>ω</mi><mo>→</mo><mn>0</mn></math></span>, this manifold is deformed into the covariant phase space <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> of a free relativistic particle, where <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup><mo>∪</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> is a two-sheeted hyperboloid in momentum space. Quantization of this model with <span><math><mi>ω</mi><mo>≠</mo><mn>0</mn></math></span> leads to the Klein-Gordon oscillator equation which we consider in the Segal-Bargmann representation. It is shown that the general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic (for antiparticles) functions on the Kähler-Einstein manifold <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>6</mn></mrow></msub></math></span>. This relativistic model is Lorentz covariant, unitary and does not contain non-physical states.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105368"},"PeriodicalIF":1.6,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hom-actions and class equation for Hom-groups 同域群的同作用和类方程
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-13 DOI: 10.1016/j.geomphys.2024.105371
Zoheir Chebel , Hadjer Adimi , Hassane Bouremel
{"title":"Hom-actions and class equation for Hom-groups","authors":"Zoheir Chebel ,&nbsp;Hadjer Adimi ,&nbsp;Hassane Bouremel","doi":"10.1016/j.geomphys.2024.105371","DOIUrl":"10.1016/j.geomphys.2024.105371","url":null,"abstract":"<div><div>The notion of Hom-groups is defined as a generalization of a non-associative group. They can be obtained by twisting the associative operation with a compatible bijection mapping. In this article, we provide some constructions by twisting and also discuss properties related to Hom-groups. We introduce different notions of actions concerning Hom-groups. We then present a theorem for a class equation, which is proven. Following that, we illustrate some applications for <em>p</em>-Hom groups.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105371"},"PeriodicalIF":1.6,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tau functions of modified CKP hierarchy 修改后的 CKP 层次结构的 Tau 功能
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-13 DOI: 10.1016/j.geomphys.2024.105367
Shen Wang , Wenchuang Guan , Jipeng Cheng
{"title":"Tau functions of modified CKP hierarchy","authors":"Shen Wang ,&nbsp;Wenchuang Guan ,&nbsp;Jipeng Cheng","doi":"10.1016/j.geomphys.2024.105367","DOIUrl":"10.1016/j.geomphys.2024.105367","url":null,"abstract":"<div><div>Modified CKP (mCKP) hierarchy is an important integrable hierarchy, that is related to CKP hierarchy through Miura link. It has been proven that there exists a tau pair <span><math><mo>(</mo><msub><mrow><mi>τ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span> for mCKP hierarchy. Further we find that mCKP hierarchy can be fully determined by CKP tau function and corresponding CKP eigenfunction. Based on this, we construct mCKP tau functions by CKP Darboux transformations and also present the vacuum expectation value of free bosons. As a byproduct, determinant formula for <span><math><mo>〈</mo><mn>1</mn><mo>|</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>H</mi><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>)</mo></mrow></msup><msub><mrow><mi>β</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><msubsup><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><msubsup><mrow><mi>β</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>⋯</mo><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><msubsup><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mi>g</mi><mo>|</mo><mn>0</mn><mo>〉</mo></math></span> is also derived.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105367"},"PeriodicalIF":1.6,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Kostant-Souriau prequantization of scalar fields with polysymplectic structures 关于具有多折射结构的标量场的科斯坦-索里奥预量化
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-12 DOI: 10.1016/j.geomphys.2024.105365
Tom McClain
{"title":"On the Kostant-Souriau prequantization of scalar fields with polysymplectic structures","authors":"Tom McClain","doi":"10.1016/j.geomphys.2024.105365","DOIUrl":"10.1016/j.geomphys.2024.105365","url":null,"abstract":"<div><div>In this paper, I present a novel, purely differential geometric approach to the quantization of scalar fields, with a special focus on the familiar case of Minkowski spacetimes. This approach is based on using the natural geometric structures of polysymplectic Hamiltonian field theory to produce an analog of the Kostant-Souriau prequantization map familiar from geometric quantization. I show that while the resulting operators are quite different from those of canonical quantum field theory, the approach is nonetheless able to reproduce a few of canonical quantum field theory's most fundamental results. I finish by elaborating the current limitations of this approach and briefly discussing future prospects.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105365"},"PeriodicalIF":1.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Baryogenesis in Minkowski spacetime 闵科夫斯基时空中的重力发生
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-07 DOI: 10.1016/j.geomphys.2024.105346
Felix Finster, Marco van den Beld-Serrano
{"title":"Baryogenesis in Minkowski spacetime","authors":"Felix Finster,&nbsp;Marco van den Beld-Serrano","doi":"10.1016/j.geomphys.2024.105346","DOIUrl":"10.1016/j.geomphys.2024.105346","url":null,"abstract":"<div><div>Based on a mechanism originally suggested for causal fermion systems, the present paper paves the way for a rigorous treatment of baryogenesis in the language of differential geometry and global analysis. Moreover, a formula for the rate of baryogenesis in Minkowski spacetime is derived.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105346"},"PeriodicalIF":1.6,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transposed Poisson structures on Virasoro-type algebras 维拉索类代数上的反转泊松结构
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-06 DOI: 10.1016/j.geomphys.2024.105356
Ivan Kaygorodov , Abror Khudoyberdiyev , Zarina Shermatova
{"title":"Transposed Poisson structures on Virasoro-type algebras","authors":"Ivan Kaygorodov ,&nbsp;Abror Khudoyberdiyev ,&nbsp;Zarina Shermatova","doi":"10.1016/j.geomphys.2024.105356","DOIUrl":"10.1016/j.geomphys.2024.105356","url":null,"abstract":"<div><div>We compute <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>-derivations on the deformed generalized Heisenberg-Virasoro<span><span><sup>1</sup></span></span> algebras and on not-finitely graded Heisenberg-Virasoro algebras <span><math><mover><mrow><mi>W</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, <span><math><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, and <span><math><mover><mrow><mi>H</mi><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. We classify all transposed Poisson structures on such algebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105356"},"PeriodicalIF":1.6,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite orbits of the braid group actions 辫状群作用的有限轨道
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-05 DOI: 10.1016/j.geomphys.2024.105363
Jialin Zhang
{"title":"Finite orbits of the braid group actions","authors":"Jialin Zhang","doi":"10.1016/j.geomphys.2024.105363","DOIUrl":"10.1016/j.geomphys.2024.105363","url":null,"abstract":"<div><div>We study the finite orbits of the braid group <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> action on the space of <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> upper-triangular matrices with 1's along the diagonal. On one hand, we give a necessary condition for a matrix <em>M</em> to be in a finite orbit; on the other hand, we classify and provide lengths of finite orbits in low-dimensional matrices and some other important cases. As the finite orbits on <span><math><mn>3</mn><mo>×</mo><mn>3</mn></math></span> matrix were crucial to finding the algebraic solutions of the sixth Painlevé equation, we hope the finite orbits on generic <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices to be useful to finding solutions of higher order Painlevé type differential equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105363"},"PeriodicalIF":1.6,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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