Light-cone thermodynamics: purification of the Minkowski vacuum

TL;DR

This paper explicitly expresses the Minkowski vacuum state of a massless scalar field in terms of particle notions associated with spherical conformal Killing fields, revealing quantum features analogous to black hole horizons.

Contribution

It provides an explicit expression of the Minkowski vacuum in terms of spherical conformal Killing fields, extending the analogy with black hole horizon thermodynamics.

Findings

Explicit vacuum decomposition in spherical conformal Killing fields

Highlights quantum aspects of horizon analogy

Extends known results beyond Rindler modes

Abstract

We explicitly express the Minkowski vacuum of a massless scalar field in terms of the particle notion associated with suitable spherical conformal killing fields. These fields are orthogonal to the light wavefronts originating from a sphere with a radius of $r_{H}$ in flat spacetime: a bifurcate conformal killing horizon that exhibits semiclassical features similar to those of black hole horizons and Cauchy horizons of spherically symmetric black holes. Our result highlights the quantum aspects of this analogy and extends the well-known decomposition of the Minkowski vacuum in terms of Rindler modes, which are associated with the boost Killing field normal to a pair of null planes in Minkowski spacetime (the basis of the Unruh effect). While some features of our result have been established by Kay and Wald's theorems in the 90s -- on quantum field theory in stationary spacetimes with bifurcate Killing horizons -- the added value we provide here lies in the explicit expression of the vacuum.