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Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020)最新文献

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Electromagnetic knots from de Sitter space 德西特空间的电磁结
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 2021-02-26 DOI: 10.22323/1.394.0011
O. Lechtenfeld
{"title":"Electromagnetic knots from de Sitter space","authors":"O. Lechtenfeld","doi":"10.22323/1.394.0011","DOIUrl":"https://doi.org/10.22323/1.394.0011","url":null,"abstract":"We find all analytic SU(2) Yang–Mills solutions on de Sitter space by reducing the field equations to Newton’s equation for a particle in a particular 3d potential and solving the latter in a special case. In contrast, Maxwell’s equations on de Sitter space can be solved in generality, by separating them in hysperspherical coordinates. Employing a well-known conformal map between (half of) de Sitter space and (the future half of) Minkowski space, the Maxwell solutions are mapped to a complete basis of rational electromagnetic knot configurations. We discuss some of their properties and illustrate the construction method with two nontrivial examples given by rational functions of increasing complexity. The material is partly based on [1, 2].","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"218 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132228375","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}
引用次数: 0
Universal dimensions of simple Lie algebras and configurations of points and lines 简单李代数的普遍维数和点与线的构形
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0005
M. Avetisyan
{"title":"Universal dimensions of simple Lie algebras and configurations of points and lines","authors":"M. Avetisyan","doi":"10.22323/1.394.0005","DOIUrl":"https://doi.org/10.22323/1.394.0005","url":null,"abstract":"The research, conducted by Vogel in 1999, in which the tensor category, called universal Lie algebra was introduced, provided a parametrization of the simple Lie algebras by three so-called universal parameters ( α : β : γ ) - projective coordinates in Vogel plane. Subsequently, it has been shown, that several characteristics of simple Lie algebras, such as dimensions of certain representations, can be expressed in terms of these three parameters by some analytic functions, which are called universal formulae. We investigate the uniqueness of the known universal dimension formulae, i.e. the possibility of the derivation of two different functions, yielding the same outputs at the same distinguished points. We employ the recently revealed geometrical rephrasing of this problem, which links us to a completely different area of mathematics - the theory of configurations of points and lines, particularly, we derive an explicit expression for a four-by-four non-uniqueness factor, making use of a known ( 16 3 , 12 4 ) configuration, demonstrating the benefit the geometrical interpretation provides with.","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133688531","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}
引用次数: 0
Split-Quaternion Analyticity and (2 + 1)-Electrodynamics 分裂四元数分析和(2 + 1)-电动力学
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0007
M. Gogberashvili
{"title":"Split-Quaternion Analyticity and (2 + 1)-Electrodynamics","authors":"M. Gogberashvili","doi":"10.22323/1.394.0007","DOIUrl":"https://doi.org/10.22323/1.394.0007","url":null,"abstract":"It is shown that the analyticity condition, applying to the invariant construction of split quaternions, is equivalent to some system of differential equations for quaternionic spinors and vectors. Assuming that the derivatives by extra time-like coordinate of (2+2)-space of split quaternions generate triality (supersymmetric)rotations, the analyticity equations is reducedto the exact Dirac-Maxwell system in 3-dimensional Minkowski space-time.","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123725573","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}
引用次数: 5
Generating Functional for the S-Matrix in Liouville Theory 刘维尔理论中s矩阵的生成泛函
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0013
G. Jorjadze, S. Theisen
{"title":"Generating Functional for the S-Matrix in Liouville Theory","authors":"G. Jorjadze, S. Theisen","doi":"10.22323/1.394.0013","DOIUrl":"https://doi.org/10.22323/1.394.0013","url":null,"abstract":"We recently proposed a functional integral representation for the generating functional of S -matrix elements of Liouville theory on a cylinder. The functional integral is defined in terms of a non-local one-dimensional action on a circle. We review and elaborate on this proposal and subject it to non-perturbative checks.","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131076139","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}
引用次数: 1
Non-compact Complex Projective Superspaces by Hamiltonian reduction 哈密顿约化的非紧复射影超空间
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0004
E. Khastyan
{"title":"Non-compact Complex Projective Superspaces by Hamiltonian reduction","authors":"E. Khastyan","doi":"10.22323/1.394.0004","DOIUrl":"https://doi.org/10.22323/1.394.0004","url":null,"abstract":"We briefly describe some concepts of super-Hamiltonian reduction and complex projective spaces. Next, we are going to perform super-Hamiltonian reduction in a concrete case, namely to get compact and non-compact complex projective superspaces from complex (pseudo)Euclidean superspaces. Then we concentrate on the non-compact case, and specifically on the supergeneralization of 𝑁 -dimensional Klein model and the mapping of superconformal mechanics on it.","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115029764","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}
引用次数: 0
N = 2 Calogero models within superfields 超域内N = 2个Calogero模型
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0017
A. Sutulin
{"title":"N = 2 Calogero models within superfields","authors":"A. Sutulin","doi":"10.22323/1.394.0017","DOIUrl":"https://doi.org/10.22323/1.394.0017","url":null,"abstract":"","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121947804","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}
引用次数: 0
Local quartic interaction of scalars with higher spin gauge fields and commutator of linear gauge transformations 高自旋规范场标量的局部四次相互作用和线性规范变换的换向子
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0012
R. Manvelyan, M. Karapetyan
{"title":"Local quartic interaction of scalars with higher spin gauge fields and commutator of linear gauge transformations","authors":"R. Manvelyan, M. Karapetyan","doi":"10.22323/1.394.0012","DOIUrl":"https://doi.org/10.22323/1.394.0012","url":null,"abstract":"Some special case of local quartic interaction of higher spin gauge field with a scalar field is considered. The nontrivial task of construction of interacting Lagrangian for the constrained higher spin field (physical gauge) was solved using the full power of Noether’s procedure. As a byproduct linear on-field gauge transformation is obtained and the corresponding closure of commutator of transformation is analyzed. The right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions of a scalar with different higher spin symmetric tensor fields and with mixed symmetry tensor field transformations.","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132239756","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}
引用次数: 0
Helicity and infinite spin representations of the Poincare group in 6D 六维庞加莱群的螺旋度和无限自旋表示
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0014
M. Podoinitsyn
{"title":"Helicity and infinite spin representations of the Poincare group in 6D","authors":"M. Podoinitsyn","doi":"10.22323/1.394.0014","DOIUrl":"https://doi.org/10.22323/1.394.0014","url":null,"abstract":"The massless irreducible representations of the Poincaré group in the six-dimensional Minkowski space are investigated. We found convenient forms of the Casimir operators and analyzed their spectra. According to this analysis, we conclude that the helicity representation is defined by two (half-)integer numbers, while the infinite spin representation is determined by the real parameter µ 2 and one (half-)integer number.","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"197 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122349637","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}
引用次数: 0
Computation on conformal moduli of Quadrilaterals 四边形共形模的计算
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0016
Ioane Shengelia
{"title":"Computation on conformal moduli of Quadrilaterals","authors":"Ioane Shengelia","doi":"10.22323/1.394.0016","DOIUrl":"https://doi.org/10.22323/1.394.0016","url":null,"abstract":"In this paper we consider classification of general topological quadrilaterals by conformal moduli and give one possible method of the numerical computation of this conformal invariant of quadrilaterals by elliptic integral of the first kind. We clarify relation between conformal moduli and AGM and give some examples.","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125078957","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}
引用次数: 0
SU(2|1) chiral superfields and spinning models SU(2|1)手性超场与自旋模型
Proceedings of RDP online workshop "Recent Advances in Mathematical Physics" — PoS(Regio2020) Pub Date : 1900-01-01 DOI: 10.22323/1.394.0019
S. Sidorov
{"title":"SU(2|1) chiral superfields and spinning models","authors":"S. Sidorov","doi":"10.22323/1.394.0019","DOIUrl":"https://doi.org/10.22323/1.394.0019","url":null,"abstract":"We consider the coupling of dynamical and semi-dynamical (spin) multiplets described by superfields living on the generalized SU ( 2 | 1 ) , 𝑑 = 1 chiral superspace. The interaction term of both multiplets is constructed as a superpotential term, where the dynamical multiplet is defined as a chiral multiplet ( 2 , 4 , 2 ) , while the semi-dynamical multiplet is associated with a mirror multiplet ( 4 , 4 , 0 )","PeriodicalId":127771,"journal":{"name":"Proceedings of RDP online workshop \"Recent Advances in Mathematical Physics\" — PoS(Regio2020)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114390144","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}
引用次数: 0
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