Interpretation of the topological terms in gauge system

TL;DR

This paper offers a new interpretation of topological terms in gauge theories by linking their emergence to the geometric phase acquired during adiabatic evolution of gauge fields at infinity.

Contribution

It demonstrates that topological terms like Chern-Simons and Pontrjagin arise from the geometric phase in gauge systems, providing an alternative conceptual understanding.

Findings

Topological terms originate from geometric phases in gauge systems.

Adiabatic evolution of gauge fields leads to additional effective action terms.

The approach connects topological invariants with physical gauge field behavior.

Abstract

We provide an alternative interpretation for the topological terms in physics by investigating the low-energy gauge interacting system. The asymptotic behavior of the gauge field at infinity indicates that it traces out a closed loop in the infinite time interval: -infinity, + infinity. Adopting Berry's argument of geometric phase, we show that the adiabatic evolution of the gauge system around the loop results in an additional term to the effective action: the Chern-Simons term for three-dimensional spacetime, and the Pontrjagin term for the four-dimensional spacetime.