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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
On conformal collineation and almost Ricci solitons 关于保角邻接和几乎利玛窦孤子
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-11-05 DOI: 10.1016/j.geomphys.2024.105354
Adara M. Blaga , Bang-Yen Chen
{"title":"On conformal collineation and almost Ricci solitons","authors":"Adara M. Blaga ,&nbsp;Bang-Yen Chen","doi":"10.1016/j.geomphys.2024.105354","DOIUrl":"10.1016/j.geomphys.2024.105354","url":null,"abstract":"<div><div>We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci solitons with affine conformal Killing potential vector field.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105354"},"PeriodicalIF":1.6,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593032","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
Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem 纤维偏振中的量子化、马布奇射线和几何彼得-韦尔定理
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-10-31 DOI: 10.1016/j.geomphys.2024.105355
Thomas Baier , Joachim Hilgert , Oguzhan Kaya , José M. Mourão , João P. Nunes
{"title":"Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem","authors":"Thomas Baier ,&nbsp;Joachim Hilgert ,&nbsp;Oguzhan Kaya ,&nbsp;José M. Mourão ,&nbsp;João P. Nunes","doi":"10.1016/j.geomphys.2024.105355","DOIUrl":"10.1016/j.geomphys.2024.105355","url":null,"abstract":"<div><div>In this paper we use techniques of geometric quantization to give a geometric interpretation of the Peter–Weyl theorem. We present a novel approach to half-form corrected geometric quantization in a specific type of non-Kähler polarizations and study one important class of examples, namely cotangent bundles of compact connected Lie groups <em>K</em>. Our main results state that this canonically defined polarization occurs in the geodesic boundary of the space of <span><math><mi>K</mi><mo>×</mo><mi>K</mi></math></span>-invariant Kähler polarizations equipped with Mabuchi's metric, and that its half-form corrected quantization is isomorphic to the Kähler case. An important role is played by invariance of the limit polarization under a torus action.</div><div>Unitary parallel transport on the bundle of quantum states along a specific Mabuchi geodesic, given by the coherent state transform of Hall, relates the non-commutative Fourier transform for <em>K</em> with the Borel–Weil description of irreducible representations of <em>K</em>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105355"},"PeriodicalIF":1.6,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659620","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
Stable isotopy connectivity of gradient-like diffeomorphisms of 2-torus 2-Torus 的梯度样差变形的稳定同位连接性
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-10-31 DOI: 10.1016/j.geomphys.2024.105352
A.A. Nozdrinov, E.V. Nozdrinova, O.V. Pochinka
{"title":"Stable isotopy connectivity of gradient-like diffeomorphisms of 2-torus","authors":"A.A. Nozdrinov,&nbsp;E.V. Nozdrinova,&nbsp;O.V. Pochinka","doi":"10.1016/j.geomphys.2024.105352","DOIUrl":"10.1016/j.geomphys.2024.105352","url":null,"abstract":"<div><div>One of the most important problems in the theory of dynamical systems (mentioned in the Palis-Pugh list) is the construction of a stable arc between structural stable diffeomorphisms in the space of diffeomorphisms. The paper considers the gradient-like diffeomorphisms of 2-torus that induce an isomorphism of fundamental groups determined by a matrix <span><math><mo>(</mo><mtable><mtr><mtd><mo>−</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>−</mo><mn>1</mn></mtd></mtr></mtable><mo>)</mo></math></span>. We prove that all such diffeomorphisms are stable isotopy connected.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105352"},"PeriodicalIF":1.6,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659622","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
Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces 各种空间中 SU(2) 反自偶杨-米尔斯方程的直接线性化
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-10-30 DOI: 10.1016/j.geomphys.2024.105351
Shangshuai Li , Da-jun Zhang
{"title":"Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces","authors":"Shangshuai Li ,&nbsp;Da-jun Zhang","doi":"10.1016/j.geomphys.2024.105351","DOIUrl":"10.1016/j.geomphys.2024.105351","url":null,"abstract":"<div><div>The paper establishes a direct linearization scheme for the SU(2) anti-self-dual Yang-Mills (ASDYM) equation. The scheme starts from a set of linear integral equations with general measures and plane wave factors. After introducing infinite-dimensional matrices as master functions, we are able to investigate evolution relations and recurrence relations of these functions, which lead us to the unreduced ASDYM equation. It is then reduced to the ASDYM equation in the Euclidean space and two ultrahyperbolic spaces by reductions to meet the reality conditions and gauge conditions, respectively. Special solutions can be obtained by choosing suitable measures.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105351"},"PeriodicalIF":1.6,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592951","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
Cohomology and extensions of relative Rota–Baxter groups 相对罗塔-巴克斯特群的同调与扩展
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-10-30 DOI: 10.1016/j.geomphys.2024.105353
Pragya Belwal, Nishant Rathee, Mahender Singh
{"title":"Cohomology and extensions of relative Rota–Baxter groups","authors":"Pragya Belwal,&nbsp;Nishant Rathee,&nbsp;Mahender Singh","doi":"10.1016/j.geomphys.2024.105353","DOIUrl":"10.1016/j.geomphys.2024.105353","url":null,"abstract":"<div><div>Relative Rota–Baxter groups are generalisations of Rota–Baxter groups and recently shown to be intimately related to skew left braces, which are well-known to yield bijective non-degenerate solutions to the Yang–Baxter equation. In this paper, we develop an extension theory of relative Rota–Baxter groups and introduce their low dimensional cohomology groups, which are distinct from the ones known in the context of Rota–Baxter operators on Lie groups. We establish an explicit bijection between the set of equivalence classes of extensions of relative Rota–Baxter groups and their second cohomology. Further, we delve into the connections between this cohomology and the cohomology of associated skew left braces. We prove that for bijective relative Rota–Baxter groups, the two cohomologies are isomorphic in dimension two.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105353"},"PeriodicalIF":1.6,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586337","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
Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one 关于皮卡数为 1 的有理同素变种上的等变向量束的完全相交超卡勒四折
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-10-30 DOI: 10.1016/j.geomphys.2024.105348
Eunjeong Lee , Kyeong-Dong Park
{"title":"Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one","authors":"Eunjeong Lee ,&nbsp;Kyeong-Dong Park","doi":"10.1016/j.geomphys.2024.105348","DOIUrl":"10.1016/j.geomphys.2024.105348","url":null,"abstract":"<div><div>We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. By computing their Hodge numbers, we see that there exist no hyperkähler fourfolds among them. This implies that a hyperkähler fourfold represented as the zero locus of a general global section of a completely reducible equivariant vector bundle over a rational homogeneous variety of Picard number one is one of the two cases described by Beauville–Donagi and Debarre–Voisin.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105348"},"PeriodicalIF":1.6,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592953","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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