从拉格朗日看物理和几何：广义框架束上的狄拉克旋量

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-08-22 DOI:10.1016/j.geomphys.2024.105297

Jérémie Pierard de Maujouy

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引用次数: 0

摘要

我们从一个无结构可微的 10-manifold [17]出发，澄清了 Hélein 和 Vey 在框架束上提出的爱因斯坦-卡尔坦引力变分原理命题中得到的结构。得到的结构局部等价于框架束，因此我们称之为 "广义框架束"。同时，我们用一个与爱因斯坦-卡尔坦时空耦合的狄拉克旋子来丰富模型。所得到的变分方程概括了通常的爱因斯坦-卡尔坦-狄拉克场方程，即当广义框架束是标准框架束时，这些方程就意味着通常的场方程。

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Physics and geometry from a Lagrangian: Dirac spinors on a generalised frame bundle

We clarify the structure obtained in Hélein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle, starting from a structure-less differentiable 10-manifold [17]. The obtained structure is locally equivalent to a frame bundle thus we term it “generalised frame bundle”. In the same time, we enrich the model with a Dirac spinor coupled to the Einstein-Cartan spacetime. The obtained variational equations generalise the usual Einstein-Cartan-Dirac field equations in the sense that they are shown to imply the usual field equations when the generalised frame bundle is a standard frame bundle.

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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