Padmanabhan's Boundary Variational Principle for Electrodynamics and Yang-Mills Theory

TL;DR

This paper extends Padmanabhan's boundary variational principle from gravitation to electrodynamics and Yang-Mills theory, revealing new insights into dual couplings and symmetry breaking within a boundary action framework.

Contribution

It demonstrates that a boundary-only variational principle can derive Maxwell and Yang-Mills equations and explains how phenomena like dual couplings and gauge symmetry breaking emerge in this approach.

Findings

Boundary variational principle applies to electrodynamics and Yang-Mills.

Dual couplings and symmetry breaking can arise from boundary actions.

Provides a new perspective on gauge theories using boundary terms.

Abstract

In this note, we revisit a variational principle introduced by Padmanabhan for describing gravitation using a field action composed solely of a boundary term. We demonstrate that this procedure can also be applied to derive Maxwell's and Yang-Mills equations. Additionally, we find that in this boundary approach, $\mathcal{CP}$-violating dual couplings and spontaneous symmetry breaking through gauge boson masses can emerge in a manner analogous to how the cosmological constant appears in the original gravitational context.