Self-Adjoint Time Operator of a Quantum Field

TL;DR

This paper introduces a quantum field model where time is treated as a dynamical variable, leading to a self-adjoint time operator and potential implications for neutrino physics.

Contribution

It presents a novel quantum field framework with temporal vibrations, establishing a self-adjoint time operator compatible with quantum principles.

Findings

Energy quantization under on-shell mass constraint

Self-adjoint time operator compatible with Pauli's theorem

Potential relevance to neutrino physics

Abstract

We study the properties of a quantum field with time as a dynamical variable. Temporal vibrations are introduced to restore the symmetry between time and space in a matter field. The system with vibrations of matter in time and space obeys the Klein-Gordon equation and Schrodinger equation. The energy observed is quantized under the constraint that a particle's mass is on shell. This real scalar field has the same properties of a zero-spin bosonic field. Furthermore, the internal time of this system can be represented by a self-adjoint operator without contradicting the Pauli's theorem. Neutrino can be an interesting candidate for investigating the effects of these temporal and spatial vibrations because of its extremely light weight.