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

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.

30 pages, 2 figures. v4: post-publication note added

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• Smooth and sharp creation of a spherical shell for a $(3+1)$-dimensional quantum field
• Vacuum excitation by sudden appearance and disappearance of a Dirichlet wall in a cavity
• Explosive particle creation by instantaneous change of boundary condition
• Localizing quantum fields with time-dependent potentials
• Quantum kicks near a Cauchy horizon
• The cost of building a wall for a fermion
• Spatial entanglement of nonvacuum Gaussian states