Michele Arzano

Getting hot without accelerating: diamond and Milne temperature from conformal quantum mechanics

The generators of radial conformal symmetries in Minkowski space-time can be put in correspondence with the generators of time evolution in conformal quantum mechanics. Within this correspondence I show that in conformal quantum mechanics the state corresponding to the inertial vacuum for a conformally invariant field in Minkowski spacetime has the structure of a thermofield double. The latter is built from a bipartite "vacuum state” corresponding to the ground state of the generators of hyperbolic time evolution. These can evolve states only within a portion of the time domain. When such generators correspond to conformal Killing vectors mapping a causal diamond in itself and generators of dilations, the temperature of the thermofield double reproduces, respectively, the diamond temperature and the Milne temperature. This result indicates that, for conformally invariant fields, the fundamental ingredient at the basis vacuum thermal effects in flat-space time is the non-eternal nature of the lifetime of observers rather than their acceleration.