Exact Massive Solutions of Classical Massless Field Theories

TL;DR

This paper presents exact solutions to classical massless field theories, demonstrating they acquire mass dynamically and extending these solutions to quantum field theory, revealing a discrete mass spectrum.

Contribution

It provides the first exact solutions showing mass generation in classical massless fields and extends these results to quantum field theory.

Findings

Massive solutions for classical massless fields

Discrete mass spectrum in solutions

Extension to quantum field theory

Abstract

We give the exact solution of classical equation of motion of a quartic scalar massless field theory showing that this is massive and is represented by a superposition of free particle solutions with a discrete spectrum. Then we show that this is also a solution of the classical Yang-Mills field theory that is so proved acquiring mass by dynamical evolution with a corresponding discrete mass spectrum. Finally we develop quantum field theory starting with this solution.