Unified Field Equations Coupling Four Forces and Principle of Interaction Dynamics

TL;DR

This paper introduces a principle of interaction dynamics (PID) to derive unified field equations for all four fundamental forces, explaining phenomena like dark matter, dark energy, and particle decay through a novel gauge symmetry breaking mechanism.

Contribution

It proposes a new variational principle (PID) for unifying fundamental interactions based on gauge invariance and general relativity, leading to a model that explains several outstanding physics and cosmology challenges.

Findings

Unified field equations coupling four fundamental forces derived from PID.

Spontaneous gauge symmetry breaking explains mass and energy generation.

Provides solutions to dark matter, dark energy, and particle decay issues.

Abstract

The main objective of this article is to postulate a principle of interaction dynamics (PID) and to derive unified field equations coupling the four fundamental interactions based on first principles. PID is a least action principle subject to div$_A$-free constraints for the variational element with $A$ being gauge potentials. The Lagrangian action is uniquely determined by 1) the principle of general relativity, 2) the $U(1)$, $SU(2)$ and $SU(3)$ gauge invariances, 3) the Lorentz invariance, and 4) principle of principle of representation invariance (PRI), introduced in [11]. The unified field equations are then derived using PID. The unified field model spontaneously breaks the gauge symmetries, and gives rise to a new mechanism for energy and mass generation. The unified field model introduces a natural duality between the mediators and their dual mediators, and can be easily decoupled to study each individual interaction when other interactions are negligible. The unified field model, together with PRI and PID applied to individual interactions, provides clear explanations and solutions to a number of outstanding challenges in physics and cosmology, including e.g. the dark energy and dark matter phenomena, the quark confinement, asymptotic freedom, short-range nature of both strong and weak interactions, decay mechanism of sub-atomic particles, baryon asymmetry, and the solar neutrino problem.