The Rigorous Relation between Rindler and Minkowski Quantum Field Theory in the Unruh Scenario

TL;DR

This paper clarifies the relationship between Minkowski and Rindler quantum field theories in the Unruh scenario, showing the correct dual theory resides in the thermal Rindler Hilbert space and introduces new quasi-particle operators.

Contribution

It demonstrates the unitary equivalence of Minkowski and thermal Rindler QFT, correcting the traditional approach that used Rindler Fock space, and introduces novel quasi-particle operators.

Findings

The dual QFT is in the thermal Rindler Hilbert space, not Rindler Fock space.

New quasi-particle/hole operators emerge in the thermal Rindler space.

Rindler particle operators are superpositions of these fundamental operators.

Abstract

Traditionally the physics of the Unruh effect, i.e. the q.f.t. in the wedges $W_R$ or $W_L$ in Minkowski space is related to the physics in the Rindler Fock space, which is a proplematical strategy. In a careful analysis we show that the correct dual q.f.t. lives rather in the thermal Rindler Hilbert space and turns out to be unitarily equivalent to the corresponding Minkowski space theory in contrast to the Rindler Fock space theory. We show in particular that in thermal Rindler Hilbert space a new sort of objects occurs, viz., quasi-particle/hole creation/annihilation operators of thermal Rindler quasi-particles and holes, which do not have a pendant in Rindler Fock space. The ordinary Rindler particle operators are certain temperature dependent superpositions of these more fundamental operators. These new objects play a crucial role in this duality and via the unitary equivalence do have their counterparts in Minkowski q.f.t.