Microcausality and Tunneling Times in Relativistic Quantum Field Theory

TL;DR

This paper demonstrates that microcausality in relativistic quantum field theory prevents superluminal tunneling, ensuring effects of localized interventions cannot propagate faster than light, supported by numerical results for Dirac and Klein-Gordon fields.

Contribution

It proves microcausality holds during tunneling in relativistic quantum fields and shows no superluminal effects occur, combining theoretical proof with numerical simulations.

Findings

Microcausality is preserved during tunneling.

Localized interventions do not produce superluminal effects.

Numerical simulations confirm theoretical predictions.

Abstract

We show, in the framework of a space-time resolved relativistic quantum field theory approach to tunneling, that microcausality precludes superluminal tunneling dynamics. More specifically in this work dealing with Dirac and Klein-Gordon fields, we first prove that microcausality holds for such fields in the presence of a background potential. We then use this result to show that an intervention performed on a localized region of an initial wave packet subsequently scattering on a potential barrier does not result in any effect outside the light cone emanating from that region. We illustrate these results with numerical computations for Dirac fermions and Klein-Gordon bosons.