论文标题
基础张量规理论的洛伦兹不变性
Lorentz Invariance of Basis Tensor Gauge Theory
论文作者
论文摘要
基础张量规理论（BTGT）是维尔贝因领域描述威尔逊线的普通规定理论的维尔贝因模拟重新印象。经过对BTGT的简要审查后，我们阐明了与用于量化的变量相关的Lorentz组表示属性。特别是，我们表明，从满足Lorentz-Invariant u（1,3）矩阵约束的SO（1,3）表示，BTGT引入了Lorentz框架选择，以选择由u（1,3）的Cartan Subergebra生成的ABELIAN组流形，即使是量级化的cartan subergebra（即使是量级），尽管该理论是独立的。选择框架的自由可以看作是以前没有强调的BTGT的附加对称性。然后，我们展示$ S_4 $置换对称性和BTGT中自然框架字段的奇偶校验对称性如何用于构建可重新计算的规格理论，该理论引入了框架依赖性字段，但在没有任何明确的指引用框架范围内，而无需对通常的规格字段进行任何明确的引用。
Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of u(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an $S_4$ permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.
