Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 26 June 2018 / Approved: 27 June 2018 / Online: 27 June 2018 (14:26:02 CEST)

How to cite: Kühne, R. Derivation of the Local Lorentz Gauge Transformation of a Dirac Spinor Field in Quantum Einstein-Cartan Theory. Preprints 2018, 2018060446 (doi: 10.20944/preprints201806.0446.v1). Kühne, R. Derivation of the Local Lorentz Gauge Transformation of a Dirac Spinor Field in Quantum Einstein-Cartan Theory. Preprints 2018, 2018060446 (doi: 10.20944/preprints201806.0446.v1).

## Abstract

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.

## Subject Areas

Einstein-Cartan theory, quantum gravity, energy-momentum tensor, Lorentz transformations, gauge invariance, quantum field theories