Gravity based on four one-dimensional unitary gauge symmetries and the Standard Model

The Standard Model of particle physics is based on compact, finite-dimensional unitary symmetries associated with internal vector spaces of quantum fields. A similar compact and finite-dimensional unitary-symmetry-based approach to the description of gravity has remained unknown. The realization of such a symmetry can contribute to better understanding of the quantum aspects of gravity and the relation of symmetries fulfilled by the gravitational field and the quantum fields of the Standard Model. Here we derive the gauge theory of gravity using compact, finite-dimensional symmetries in a way that resembles the formulation of the fundamental interactions of the Standard Model as closely as possible [arXiv:2310.01460]. For our eight-spinor representation of the Lagrangian, we define a quantity, called the space-time dimension field, which enables extracting four-dimensional space-time quantities from the eight-dimensional spinors. We use four U(1) symmetries of the components of the space-time dimension field to derive a gauge theory, called unified gravity. The stress-energy-momentum tensor source term of gravity follows directly from these symmetries. The metric tensor enters in unified gravity through geometric conditions. We show how the teleparallel equivalent of general relativity in the Weitzenböck gauge is obtained from unified gravity by a gravity-gauge-field-dependent geometric condition. Unified gravity also enables a gravity-gauge-field-independent geometric condition that preserves the constant Minkowski metric. Consequently, we obtain an exact description of gravity in the Minkowski metric. This differs from the use of metric in general relativity, where the metric depends on the gravitational field by definition, and whose effective quantization requires expansion of the metric about the flat or smooth background. We present the Feynman rules for unified gravity and perform quantum gravity calculations for elementary scattering processes.