Quantum Fluctuations and Dynamical Chaos: An Effective Potential Approach

TL;DR

This paper explores how quantum fluctuations influence classical chaos, demonstrating that radiative effects can stabilize the vacuum and potentially prevent chaos in gauge theories.

Contribution

It introduces an effective potential approach linking quantum fluctuations to classical chaos, with specific analysis on scalar electrodynamics and implications for non-Abelian theories.

Findings

Radiative symmetry breaking stabilizes the vacuum against chaos

Quantum effects can suppress classical chaotic behavior

Monopole condensation may similarly stabilize non-Abelian gauge theories

Abstract

We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.