Quantum Restoration of Broken Symmetry in one Dimensional Loop Space

TL;DR

This paper introduces a nonlinear transformation in 1D loop space that restores broken classical symmetries at the quantum level, demonstrated through specific models like the sine-Gordon system.

Contribution

It presents a novel nonlinear nonlocal transformation that restores classical symmetry breaking in quantum 1D loop space models.

Findings

Symmetry is restored in quantum theory for certain classical broken symmetries.

The method is explicitly demonstrated on sine-Gordon and Sech interaction models.

Abstract

For 1 Dimensional loop space, a nonlinear nonlocal transformation of fields is given to make the action of the self-interacting quantum field to the free one. A specific type of Classically broken symmetry is restored in Quantum theory. 1-D Sine Gordon system and Sech interactions are treated as the explicit example.