Field Theory of Four Interactions

Abstract: In this talk, I shall present a few first principles and laws for four fundamental forces of Nature, demonstrating the symbiotic interplay between advanced mathematics and theoretical physics.

First, we present Einstein’s principle of general relativity and principle of equivalence, leading to the Einstein equations. The presence of dark matter and dark energy suggests us to postulate a new principle called the principle of interaction dynamics (PID), which takes the variation of the action functional under energy-momentum conservation constraint. With PID, we are able to derive a set of gravitational field equations, leading to a theory for dark energy and dark matter.

Second, we present the principle of gauge invariance (H. Weyl, Yang-Mills), and a new principle, called the principle of representation invariance (PRI), which requires that physical laws be independent of representations of the gauge Lie groups.

Then we shall demonstrate how these two newly postulated principles, PID and PRI, lead to a unified field theory for four forces and some interesting physical conclusions such as strong and weak interaction potentials, quark confinement and short-range nature of strong and weak interactions. The new results presented in this talk are based on joint work with Tian Ma.