Particle Production Between Isometric Frames on a Poincar\'e Patch of $\text{AdS}_2$

TL;DR

This paper investigates particle production between isometric frames in a Poincaré patch of AdS2, revealing that boundary conditions influence vacuum invariance and particle creation, with finite total particles except at boundary-invariant cases.

Contribution

It demonstrates how boundary conditions affect vacuum invariance and particle production between isometric observers in AdS2, highlighting differences from Minkowski spacetime.

Findings

Total particle number is finite for generic boundary conditions.

Particle production diverges as boundary conditions approach Dirichlet or Neumann.

Vacuum invariance occurs only at boundary-invariant conditions.

Abstract

In a recent paper [J. P. M. Pitelli, Phys. Rev. D {\bf 99}, 108701 (2019)], one of us showed that the vacuum state associated to conformal fields on a Poicar\'e patch of anti-de Sitter spacetime is not $\text{AdS}$ invariant for fields satisfying non-trivial boundary conditions (by non-trivial we mean neither Dirichlet nor Neumann) at the conformal boundary. In this way, two isometrically related observers in anti-de Sitter space have different notions of no particle content. Therefore, an observer who is suddenly transported to a different (but isometrically related) frame will feel a bath of particles. This process contradicts our intuitive notion based on our experience in Minkowski spacetime, where the vacuum is Lorentz invariant, and no particle is produced between boosted frames. We show that the total number of produced particles is finite, but grows without limit when we approach (via isometric transformation) Dirichlet or Neumann boundary conditions since in these cases the vacuum is invariant.