Four inequivalent paths to Thermality in Minkowski spacetime

TL;DR

This paper explores alternative paths to thermality in quantum fields in Minkowski spacetime, showing that thermal spectra can arise without entanglement-induced mixedness through null-shifted wedge constructions.

Contribution

It introduces null-shifted wedge transformations that produce non-Gibbsian thermal states, demonstrating thermality can be independent of entanglement and horizon effects.

Findings

Null-shifted wedges lead to single-sector Bose-Einstein thermal states.

Global Minkowski state remains pure despite local thermal behavior.

Thermality can arise from Bogoliubov transformations without entanglement.

Abstract

We investigate thermal behaviour in quantum fields by analysing a hierarchy of null-shifted Rindler wedges in Minkowski spacetime. Starting from the Minkowski vacuum restricted to an initial Rindler wedge, we construct several inequivalent transformation paths, including direct Minkowski-Rindler mappings, spatial translations, and sequential null displacements, and analyse the resulting particle content using Bogoliubov transformations. In the standard Unruh effect, entanglement between left- and right-moving sectors across the Rindler horizon produces Gibbsian thermality, with both sectors described by mixed thermal states. In contrast, we show that null-shifted wedge constructions lead to a selective and non-Gibbsian form of thermality: only a single chiral sector develops Bose-Einstein-distributed occupation numbers, while the complementary sector remains in the vacuum. Along composite transformation paths, the global Minkowski state remains pure, and the induced states associated with null-shifted wedges are pure tensor-product states. The observed thermal behaviour arises from Bogoliubov mixing and modular time evolution rather than horizon-induced entanglement or Gibbsian mixedness. These results demonstrate the existence of inequivalent purifications of thermal spectra and clarify the distinct roles of horizon structure, observer dependence, Bogoliubov transformations, and entanglement in relativistic quantum field theory. The null-shifted construction may be viewed as a converse of the Unruh effect, in which thermal spectra arise without entanglement-induced mixedness, highlighting the operational independence of thermality and entanglement.