Massive quantum scalar field theory in the presence of moving mirrors

TL;DR

This paper investigates the behavior of massive quantum scalar fields in 2D with moving mirrors, analyzing mode structures, commutation relations, and stress-energy tensor expectations for ideal and non-ideal mirrors, revealing non-canonical relations and decay effects.

Contribution

It provides a detailed analysis of massive scalar fields with moving mirrors, highlighting differences between ideal and non-ideal mirrors and their impact on field quantization and stress-energy tensor.

Findings

Non-canonical commutation relations for ideal mirrors.

Canonical relations for non-ideal, transparent mirrors.

Non-diagonal stress-energy tensor contributions decay with distance.

Abstract

We study the 2D massive fields in the presence of moving mirrors. We do that for standing mirror and mirror moving with constant velocity. We calculate the modes and commutation relations of the field operator with the corresponding conjugate momentum in each case. We find that in case of the ideal mirror, which reflects modes with all momenta equally well, the commutation relations do not have their canonical form. However, in the case of non-ideal mirror, which is transparent for the modes with high enough momenta, the commutation relations of the field operator and its conjugate momentum have their canonical form. Then we calculate the free Hamiltonian and the expectation value of the stress-energy tensor in all the listed situations. In the presence of moving mirrors the diagonal form in terms of the creation and annihilation operators has the operator that performs translations along the mirror's world line rather than the one which does translations along the time-line. For the massive fields in the presence of a mirror moving with constant velocity the expectation value of the stress-energy tensor has a non-diagonal contribution which decays with the distance from the mirror.