Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model (2310.01460v7)

Abstract: The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has been challenging due to incompatibilities of the underlying theories - general relativity and quantum field theory. While quantum field theory utilizes compact, finite-dimensional symmetries associated with the internal degrees of freedom of quantum fields, general relativity is based on noncompact, infinite-dimensional external space-time symmetries. The present work aims at deriving 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. This can contribute to improved understanding of the relation between the Standard Model and the gauge theory of gravity. For our eight-spinor representation of the Lagrangian, we define a quantity, called the space-time dimension field. Four U(1) symmetries of the space-time dimension field are used to derive a gauge theory, called unified gravity. We show how the teleparallel equivalent of general relativity in the Weitzenb\"ock 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. 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 study the theory at the tree level. The radiative corrections and renormalizability of unified gravity are left as topics of further works.