Zero mode in the time-dependent symmetry breaking of $\lambda\phi^4$ theory

TL;DR

This paper investigates the role of the zero mode in the time-dependent symmetry breaking of scalar  theory using a variational approximation, highlighting its non-trivial quantum effects.

Contribution

It introduces a method to treat the zero mode quantum mechanically in time-dependent symmetry breaking analysis of  scalar field theory.

Findings

Zero mode significantly influences symmetry breaking dynamics.

Quantum properties of the zero mode are non-trivial.

Effective potential and action are derived with zero mode treatment.

Abstract

We apply the quartic exponential variational approximation to the symmetry breaking phenomena of scalar field in three and four dimensions. We calculate effective potential and effective action for the time-dependent system by separating the zero mode from other non-zero modes of the scalar field and treating the zero mode quantum mechanically. It is shown that the quantum mechanical properties of the zero mode play a non-trivial role in the symmetry breaking of the scalar $\lambda \phi^4$ theory.