Time and energy operators in the canonical quantization of special relativity

TL;DR

This paper explores how Lorentz and Born reciprocity invariances in special relativity's canonical quantization unify quantum mechanics' mathematical structure, commutation relations, the Dirac Hamiltonian, and introduce a self-adjoint Time Operator.

Contribution

It demonstrates that these invariances lead to a unified foundation for quantum mechanics and relativistic quantum mechanics, including a self-adjoint Time Operator.

Findings

Unified origin for quantum mechanics and special relativity

Derivation of the Dirac Hamiltonian from invariances

Introduction of a self-adjoint Time Operator

Abstract

Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) is shown to provide a unified origin for: i) the complex vector space formulation of Quantum Mechanics (QM); ii) the momentum and space commutation relations and the corresponding representations; iii) the Dirac Hamiltonian in the formulation of Relativistic Quantum Mechanics (RQM); iv) the existence of a self adjoint Time Operator that circumvents Pauli's objection.