六维自旋 3/2 的无质量场方程

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-10-15 DOI:10.1016/j.geomphys.2024.105341

R. Lávička , V. Souček , W. Wang

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引用次数: 0

摘要

本文的主要议题是研究自旋 3/2 的无质量场的性质。关于维度 4 的无质量场，我们已经掌握了大量信息。在此，我们集中研究维度 6，并利用 SL(4,C) 群与 Spin(6,C) 群同构这一事实。这使得无质量场有可能使用张量形式主义。论文中讨论的主要问题包括：需要在自旋 3/2 情况下考虑的场的描述、它们应该满足的方程的合适选择、无质量场方程同质解的不可还原性、费舍分解和这类场的豪厄对偶性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Massless field equations for spin 3/2 in dimension 6

Main topic of the paper is a study of properties of massless fields of spin 3/2. A lot of information is available already for massless fields in dimension 4. Here, we concentrate on dimension 6 and we are using the fact that the group

S L (4, C)

is isomorphic with the group

S p i n (6, C)

. It makes it possible to use tensor formalism for massless fields. Main problems treated in the paper are a description of fields which need to be considered in the spin 3/2 case, a suitable choice of equations they should satisfy, irreducibility of homogeneous solutions of massless field equations, the Fischer decomposition and the Howe duality for such fields.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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