Quantum corrections to tunnelling amplitudes of neutral scalar fields

TL;DR

This paper explores how quantum field theory corrections influence tunnelling probabilities of neutral scalar fields in external potentials, extending single-particle quantum mechanics to include many-particle effects like pair-production.

Contribution

It formulates an all-order recursive expression for loop-corrected scalar propagators with vertex corrections, applicable to general external potentials.

Findings

Derived a recursive equation for loop-corrected propagators

Demonstrated perturbative approximation methods for QFT corrections

Extended tunnelling analysis to include quantum field effects

Abstract

Though theoretical treatments of quantum tunnelling within single-particle quantum mechanics are well-established, at present, there is no quantum field-theoretic description (QFT) of tunnelling. Due to the single-particle nature of quantum mechanics, many-particle effects arising from quantum field theory are not accounted for. Such many-particle effects, including pair-production, have proved to be essential in resolving the Klein-paradox. This work seeks to determine how quantum corrections affect the tunnelling probability through an external field. We investigate a massive neutral scalar field, which interacts with an external field in accordance with relativistic quantum mechanics. To consider QFT corrections, we include another massive quantised neutral scalar field coupling to the original via a cubic interaction. This study formulates an all-order recursive expression for the loop-corrected scalar propagator, which contains only the class of vertex-corrected Feynman diagrams. This equation applies for general external potentials. Though there is no closed-form analytic solution, we also demonstrate how to approximate the QFT corrections if a perturbative coupling to the quantised field is assumed.