Complex Charges, Time Reversal Asymmetry, and Interior-Boundary Conditions in Quantum Field Theory

TL;DR

This paper investigates the conditions under which non-relativistic quantum field theory Hamiltonians involving particle creation and annihilation are time asymmetric, especially when charges are complex, affecting symmetry and ground state properties.

Contribution

It introduces criteria for time reversal symmetry breaking in QFT Hamiltonians with complex charges using Bohmian trajectories and interior-boundary conditions.

Findings

Time reversal symmetry can be broken with complex charges.

Ground states may exhibit non-zero probability currents.

Effective potentials between fermions depend on charge phase.

Abstract

While fundamental physically realistic Hamiltonians should be invariant under time reversal, time asymmetric Hamiltonians can occur as mathematical possibilities or effective Hamiltonians. Here, we study conditions under which non-relativistic Hamiltonians involving particle creation and annihilation, as come up in quantum field theory (QFT), are time asymmetric. It turns out that the time reversal operator T can be more complicated than just complex conjugation, which leads to the question which criteria determine the correct action of time reversal. We use Bohmian trajectories for this purpose and show that time reversal symmetry can be broken when charges are permitted to be complex numbers, where `charge' means the coupling constant in a QFT that governs the strength with which a fermion emits and absorbs bosons. We pay particular attention to the technique for defining Hamiltonians with particle creation based on interior-boundary conditions, and we find them to generically be time asymmetric. Specifically, we show that time asymmetry for complex charges occurs whenever not all charges have equal or opposite phase. We further show that, in this case, the corresponding ground states can have non-zero probability currents, and we determine the effective potential between fermions of complex charge.