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arXiv 2303.05366gr-qchep-th
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庞加莱规范场理论四讲

Four Lectures on Poincaré Gauge Field Theory

Friedrich W. Hehl

摘要:

庞加莱(非齐次洛伦兹)群是狭义相对论的基础。在这些讲座一致的形式主义发展允许适当衡量庞加莱集团。物理定律是用点、正交四元框架和相对于这些框架的物质场分量来表述的。该定律被假定为在局部庞加莱变换下是规范不变的。这意味着存在4个平移规范势${e}^α$("引力子”)和6个洛伦兹规范势$Γ^{αβ}$("回旋子”)以及物质的动量流和自旋流分别与这些规范势的耦合。这样我们就得到了一个带有挠率和曲率的黎曼-嘉当时空,它的结构比广义相对论的时空更丰富。黎曼-嘉当时空由两个一般的规范场方程(3.44)和(3.45)控制,其中物质的动量和自旋作为源。该理论的总体框架在3.6节的表格中进行了总结。--讨论了选取规范场拉格朗日量的选项(远程并行,ECSK)。我们提出了一个关于挠率和曲率的拉格朗日二次方程来控制引力子和转动子的传播。对旋子的抑制又回到了广义相对论。

英文摘要:

The Poincaré (inhomogeneous Lorentz) group underlies special relativity. In these lectures a consistent formalism is developed allowing an appropriate gauging of the Poincaré group. The physical laws are formulated in terms of points, orthonormal tetrad frames, and components of the matter fields with respect to these frames. The laws are postulated to be gauge invariant under local Poincaré transformations. This implies the existence of 4 translational gauge potentials ${e}^α$ (``gravitons") and 6 Lorentz gauge potentials $Γ^{αβ}$ (``rotons") and the coupling of the momentum current and the spin current of matter to these potentials, respectively. In this way one is led to a Riemann-Cartan spacetime carrying torsion and curvature, richer in structure than the spacetime of general relativity. The Riemann-Cartan spacetime is controlled by the two general gauge field equations (3.44) and (3.45), in which material momentum and spin act as sources. The general framework of the theory is summarized in a table in Section 3.6. -- Options for picking a gauge field lagrangian are discussed (teleparallelism, ECSK). We propose a lagrangian quadratic in torsion and curvature governing the propagation of gravitons and rotons. A suppression of the rotons leads back to general relativity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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