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

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.