Re-Interpretation of Spontaneous Symmetry Breaking in Quantum Field Theory and Goldstone Theorem

TL;DR

This paper re-examines spontaneous symmetry breaking in quantum field theory, showing that the fermion condensate can vanish in exact solutions, challenging the traditional Goldstone theorem application, exemplified by the Thirring model.

Contribution

It introduces a new perspective on symmetry breaking by focusing on conserved charges and demonstrates that fermion condensates may vanish in exact solutions, questioning established interpretations.

Findings

Fermion condensate vanishes in exact solutions of certain models.

Goldstone theorem may not apply when condensates are zero.

Thirring model exemplifies spontaneous symmetry breaking without condensate.

Abstract

We present a new picture of global symmetry breaking in quantum field theory and propose a novel realization of symmetry breaking phenomena in terms of the conserved charge associated with its symmetry. In particular, the fermion condensate of the vacuum state is examined when the spontaneous chiral symmetry breaking takes place. It is shown that the fermion condensate of the vacuum vanishes if the system is solved exactly, and therefore we cannot make use of the Goldstone theorem. As a perfect example, we present the Bethe ansatz vacuum of the Thirring model which shows the spontaneous chiral symmetry breaking with no fermion condensate.