Families of particles with different masses in PT-symmetric quantum field theory

TL;DR

This paper proposes a mechanism in PT-symmetric quantum field theory where a single Lagrangian can describe a family of particles with different masses, based on multiple solutions to Dyson-Schwinger equations in complex field space.

Contribution

It introduces a novel approach linking non-unique Dyson-Schwinger solutions to PT symmetry, enabling a single Lagrangian to represent particles with varying masses.

Findings

Multiple solutions to Dyson-Schwinger equations exist in PT-symmetric QFT.

Solutions are physically valid when associated with PT-symmetric Stokes' wedges.

The mechanism allows a single Lagrangian to describe a family of particles with different masses.

Abstract

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.