Quantum Origin of (Newtonian) Mass and Symmetry for Lorentz Covariant Physics

TL;DR

This paper explores the quantum origin of mass and symmetry in Lorentz covariant physics, proposing a group theoretical framework that revises the understanding of mass as a Casimir invariant and discusses limitations of Poincare symmetry.

Contribution

It introduces a novel group theoretical formulation that redefines the role of mass and examines the limitations of Poincare symmetry in relativistic physics.

Findings

Mass identified as a Casimir invariant in the new framework

Revised understanding of Lorentz covariant symmetries

Discussion on limitations of Poincare symmetry

Abstract

The Galilean symmetry and the Poincare symmetry are usually taken as the fundamental (relativity) symmetries for `nonrelativistic' and `relativistic' physics, respectively, quantum or classical. Our fully group theoretical formulation approach to the theories, together with its natural companion of mechanics from symplectic geometry, ask for different perspectives. We present a sketch of the full picture here, emphasizing aspects which are different from the more familiar picture. The letter summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or corrected, identification of the basic representations having the (Newtonian) mass as a Casimir invariant. Discussion on the limitations of the Poincare symmetry for the purpose is particularly elaborated.