Gravitization Equation and Zero Energy Momentum Tensor Theorem with Cancellation Law in Gravitational Quantum Field Theory

TL;DR

This paper develops a gravitational quantum field theory based on spin gauge symmetry, deriving a gravitization equation and demonstrating a zero energy-momentum tensor theorem, with implications for quantum gravity and three-dimensional spacetime models.

Contribution

It introduces a new gravitization equation and establishes a zero energy-momentum tensor theorem in GQFT, connecting gravitational effects with gauge symmetry and quantum field theory.

Findings

Derivation of a gravitization equation from spin gauge symmetry.

Demonstration that the energy-momentum tensor vanishes in GQFT under equations of motion.

Development of a GQFT with Chern-Simons action in three-dimensional spacetime.

Abstract

We investigate the essential properties of gravitational quantum field theory (GQFT) based on spin gauge symmetry, using the general theory of quantum electrodynamics as an example. A constraint equation for the field strength of the gravigauge field is derived, serving as a gravitization equation within the spin-related gravigauge spacetime. This equation reveals how gravitational effects emerge from the non-commutative relation of the gravigauge derivative operator. By transmuting the action from gravigauge spacetime to Minkowski spacetime, we demonstrate that translational invariance results in a vanishing energy-momentum tensor in GQFT when the equations of motion are applied to all fundamental fields, including the gravigauge field. This extends the conservation law of the energy-momentum tensor in quantum field theory to a cancellation law of the energy-momentum tensor in GQFT. As a result, an equivalence between the general gravitational equation and the zero energy-momentum tensor theorem naturally arises in GQFT. Certain aspects of the Poincar\'e gauge theory are also briefly discussed. Furthermore, a GQFT incorporating the Chern-Simons action in three-dimensional spacetime is developed, based on the inhomogeneous spin gauge symmetry WS(1,2) and the global Poincar\'e symmetry PO(1,2). This framework provides a basis for exploring its connection to Witten's perspective on three-dimensional gravity.