Extraordinary Invariants are Seeds that Grow Interacting Theories Out of Free Theories

TL;DR

This paper explores how Extraordinary Invariants in BRST Cohomology act as seeds that transform free theories into interacting theories, exemplified by deriving Yang-Mills theory and suggesting potential for discovering new theories.

Contribution

It introduces a novel mechanism where Extraordinary Invariants generate interacting theories from free theories within the BRST framework, revealing new pathways for theory construction.

Findings

Yang-Mills theory is derived from free gauge theory using BRST cohomology.

Extraordinary Invariants serve as seeds for growing interacting theories.

The method can potentially uncover new theories, including in supersymmetry.

Abstract

Extraordinary Invariants are elements of the BRST Cohomology Space which are irrevocably dependent on Zinn sources. The existence of an Extraordinary Invariant means that the symmetry is broken in that sector, and that the field equations can almost rescue the invariance. Adding the Extraordinary Invariant to the action results in a new theory with constraints on the starting theory. So Extraordinary Invariants are seeds from which a theory can grow. For a simple example, it is shown in this paper how Yang Mills theory is implicitly contained in the BRST Cohomology of Free Gauge Theory. It comes from an Extraordinary Invariant which can be added to the free gauge action. The Jacobi Identities are generated by requiring that the BRST Poisson Bracket be zero. Since the mechanism is a general one, it can be used to construct new theories. Some of these, for example in Supersymmetric theories, have not yet been noticed using other methods.