Relativistic Quantum Field Theory Approach to Wavepacket Tunneling: Lack of Superluminal Transmission

TL;DR

This paper uses relativistic quantum field theory to analyze electron wavepacket tunneling, demonstrating that the process is fully causal and rules out superluminal transmission, even in cases like Klein tunneling.

Contribution

It establishes a link between micro-causality in QFT and wavepacket behavior, providing a rigorous proof that tunneling cannot be superluminal.

Findings

Tunneling dynamics are fully causal, with no superluminal effects.

Numerical simulations confirm wavepackets stay within the causal light cone.

Superluminal transmission claims are refuted by QFT analysis.

Abstract

We investigate relativistic wavepacket dynamics for an electron tunneling through a potential barrier employing space-time resolved solutions to relativistic quantum field theory (QFT) equations. We prove by linking the QFT property of micro-causality to the wavepacket behavior that the tunneling dynamics is fully causal, precluding instantaneous or superluminal effects that have recently been reported in the literature. We illustrate these results by performing numerical computations for an electron tunneling through a potential barrier for standard tunneling as well for Klein tunneling. In all cases (Klein tunneling \ or regular tunneling across a standard or a supercritical potential) the transmitted wavepacket remains in the causal envelope of the propagator, even when its average position lies ahead of the average position of the corresponding freely propagated wavepacket.