# American Institute of Mathematical Sciences

March  2015, 35(3): 1103-1138. doi: 10.3934/dcds.2015.35.1103

## Unified field equations coupling four forces and principle of interaction dynamics

 1 Department of Mathematics, Sichuan University, Chengdu 2 Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  January 2013 Revised  July 2014 Published  October 2014

The main objective of this article is to postulate a principle of interaction dynamics (PID) and to derive 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) the principle of representation invariance (PRI), introduced in [11]. The unified field equations are then derived using PID. The field model spontaneously breaks the gauge symmetries, and gives rise to a new mass generation mechanism. 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.
Citation: Tian Ma, Shouhong Wang. Unified field equations coupling four forces and principle of interaction dynamics. Discrete & Continuous Dynamical Systems, 2015, 35 (3) : 1103-1138. doi: 10.3934/dcds.2015.35.1103
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