Smooth and sharp creation of a Dirichlet wall in 1+1 quantum field theory: how singular is the sharp creation limit?

TL;DR

This paper develops a formalism for smoothly creating boundary conditions in 1+1 quantum field theory, revealing how the energy flux behaves during the process and exploring implications for black hole physics.

Contribution

It introduces a simple method to model smooth boundary creation in quantum fields and analyzes the associated energy flux and divergences, extending prior perturbative results.

Findings

Finite stress-energy tensor with infrared cutoff

Ultraviolet divergence in instantaneous creation

Finite detector response despite infinite energy burst

Abstract

We present and utilize a simple formalism for the smooth creation of boundary conditions within relativistic quantum field theory. We consider a massless scalar field in $(1+1)$-dimensional flat spacetime and imagine smoothly transitioning from there being no boundary condition to there being a two-sided Dirichlet mirror. The act of doing this, expectantly, generates a flux of real quanta that emanates from the mirror as it is being created. We show that the local stress-energy tensor of the flux is finite only if an infrared cutoff is introduced, no matter how slowly the mirror is created, in agreement with the perturbative results of Obadia and Parentani. In the limit of instantaneous mirror creation the total energy injected into the field becomes ultraviolet divergent, but the response of an Unruh-DeWitt particle detector passing through the infinite burst of energy nevertheless remains finite. Implications for vacuum entanglement extraction and for black hole firewalls are discussed.