Derivation of the Local Lorentz Gauge Transformation of a Dirac Spinor Field in Quantum Einstein-Cartan Theory

I examine the groups which underly classical mechanics, non-relativistic quantum mechanics, special relativity, relativistic quantum mechanics, quantum electrodynamics, quantum flavourdynamics, quantum chromodynamics, and general relativity. This examination includes the rotations SO(2) and SO(3), the Pauli algebra, the Lorentz transformations, the Dirac algebra, and the U(1), SU(2), and SU(3) gauge transformations. I argue that general relativity must be generalized to Einstein-Cartan theory, so that Dirac spinors can be described within the framework of gravitation theory.

本文研究了构成经典力学、非相对论量子力学、狭义相对论、相对论量子力学、量子电动力学、量子味动力学、量子色动力学以及广义相对论之基础的各类群。本研究涵盖特殊正交群SO(2)与SO(3)、泡利代数（Pauli algebra）、洛伦兹变换（Lorentz transformations）、狄拉克代数（Dirac algebra），以及U(1)、SU(2)和SU(3)规范变换。本文提出，需将广义相对论推广至爱因斯坦-嘉当理论（Einstein-Cartan theory），从而能够在引力理论框架内描述狄拉克旋量（Dirac spinors）。