Modal Hamiltonian interpretation of quantum mechanics and Casimir operators: the road towards quantum field theory

TL;DR

This paper extends the Modal-Hamiltonian interpretation of quantum mechanics to relativistic contexts, proposing Casimir operators as actual-valued observables and ensuring consistency across non-relativistic and relativistic limits.

Contribution

It introduces a novel approach by identifying Casimir operators as actual observables in relativistic quantum mechanics within the Modal-Hamiltonian framework.

Findings

Casimir operators serve as actual-valued observables in relativistic quantum mechanics.

The proposed interpretation maintains consistency between relativistic and non-relativistic limits.

Extension of the Modal-Hamiltonian interpretation to gauge fields and quantum field theory contexts.

Abstract

The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) elds. In this case we propose that the actual- valued observables are the Casimir operators of the Poincar\'e group and of the group U(1) of the internal symmetry of the theory. Moreover, we also show that the magnitudes that acquire actual values in the relativistic and in the non-relativistic cases are correctly related through the adequate limit.