Vacuum thermal effects in flat space-time from conformal quantum mechanics

TL;DR

This paper demonstrates that vacuum thermal effects in flat space-time can be understood through conformal quantum mechanics, linking horizon presence to perceived temperature without requiring acceleration.

Contribution

It provides a group theoretical derivation of Milne and diamond temperatures, emphasizing horizons as the key to vacuum thermal effects rather than acceleration.

Findings

Vacuum state has a thermofield double structure in conformal quantum mechanics.

Finite time domain evolution leads to perceived temperature by observers.

Horizon presence, not acceleration, is fundamental for thermal effects.

Abstract

The generators of radial conformal symmetries in Minkowski space-time can be mapped to the generators of time evolution in conformal quantum mechanics. Within this correspondence we show that in conformal quantum mechanics the state associated to the inertial vacuum in Minkowski space-time has the structure of a thermofield double. Such state is built from a bipartite "vacuum state", the ground state of the generators of hyperbolic time evolution, which cover only part of the time domain. When time evolution is restricted to a finite time domain one obtains the temperature perceived by static diamond observers in the Minkowski vacuum. When time evolution is determined by dilations, covering only half of the time line, the temperature of the thermofield double corresponds to the non-vanishing temperature perceived by Milne observers whose proper time evolution is confined to the future cone (Milne universe) of Minkowski space-time. The two pictures are related by a conformal transformation on the real line. Our result provides a purely group theoretical derivation of the Milne and diamond temperature and shows that the fundamental ingredient for vacuum thermal effects is the presence of a horizon rather than acceleration.