Second quantization of time and energy in Relativistic Quantum Mechanics

TL;DR

This paper develops a second quantization framework for time and energy in relativistic quantum mechanics, unifying space-time treatment and introducing the concept of time quanta with potential applications in quantum gravity and cold atom systems.

Contribution

It presents a novel second quantization approach for the time operator in relativistic quantum mechanics, linking it to quantum field theory concepts.

Findings

Restores symmetric treatment of space and time in QM

Introduces the concept of time quanta analogous to energy quanta

Highlights potential relevance to quantum gravity and cold atom physics

Abstract

Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) has been shown to provide a unified origin for the existence of Dirac's Hamiltonian and a self adjoint time operator that circumvents Pauli's objection. As such, this approach restores to Quantum Mechanics (QM) the treatment of space and time on an equivalent footing as that of momentum and energy. Second quantization of the time operator field follows step by step that of the Dirac Hamiltonian field. It introduces the concept of time quanta, in a similar way to the energy quanta in Quantum Field Theory (QFT). An early connection is found allready in Feshbach's unified theory of nuclear reactions. Its possible relevance in current developments such as Feshbach resonances in the fields of cold atom systems, of Bose-Einstein condensates and in the problem of time in Quantum Gravity is noted. .