A Classical and Quantum Relativistic Interacting Variable-Mass Model

Abstract

A classical and quantum relativistic interacting particle formalism is revisited. A Hilbert space is achieved through the use of variable individual particle rest masses, but no c-number mass parameter is required for the relativistic free particle. Boosted center of momentum states feature in both the free and interacting model. The implications of a failure to impose simultaneity conditions at the classical level are explored. The implementation of these conditions at the quantum level leads to a finite uncertainty in interaction times, perhaps more closely modeling the exchange of virtual particles in quantum field theory. This work is compared and contrasted with other variable mass models in the literature.