No resonant tunneling in standard scalar quantum field theory

Abstract

We investigate the nature of resonant tunneling in Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu, we describe quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path'' (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.

arXiv commentSection added and both introduction and conclusions expanded in order to clarify a number of points. References added. Minor change to title

References in corpus (6)

• Oscillons: Resonant Configurations During Bubble Collapse
• An Open Universe from Inflation
• Pseudo-Stable Bubbles
• Oscillons and quasi-breathers in D+1 dimensions
• Vacuum decay in quantum field theory
• Tunneling in a quantum field theory on a compact one-dimensional space

Cited by in corpus (9)

• Dark Energy
• A parton picture of de Sitter space during slow-roll inflation
• Cosmological Constant from Decoherence
• Tunneling and propagation of vacuum bubbles on dynamical backgrounds
• Schwinger effect and false vacuum decay as quantum-mechanical tunneling of a relativistic particle
• A-B transition in superfluid ${}^3$He and cosmological phase transitions
• Generalised escape paths for dynamical tunneling in QFT
• On the fate of vacuum bubbles on matter backgrounds
• The WKB approximation and tunneling in theories with non-canonical kinetic terms