Varying the Unruh temperature in integrable quantum field theories

Abstract

A computational scheme is developed to determine the response of a quantum field theory (QFT) with a factorized scattering operator under a variation of the Unruh temperature. To this end a new family of integrable systems is introduced, obtained by deforming such QFTs in a way that preserves the bootstrap S-matrix. The deformation parameter β plays the role of an inverse temperature for the thermal equilibrium states associated with the Rindler wedge, β = 2π being the QFT value. The form factor approach provides an explicit computational scheme for the β = 2π systems, enforcing in particular a modification of the underlying kinematical arena. As examples deformed counterparts of the Ising model and the Sinh-Gordon model are considered.

Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation

“…In this section we review the results of [14,15,16] and state the modified form factor equations. The starting point is the Bisignano-Wichmann-Unruh thermalisation phenomenon stating that the vacuum of a Minkowski space QFT looks like a thermal state of inverse temperature β = 2π with respect to the Killing time of the Rindler wedge [1,26].…”

“…Here K stands for the generator of Lorentz boosts in W . Note that this trace can -in contrast to lattice models -never exist in a continuum QFT due to the noncompactness of K as described in [14,16]. We therefore take (4) only as a mnemonic.…”

“…For example naively regularizing the trace in (4) would most likely lead to enormous technical problems with renormalizability since the translation invariance of the original QFT is lost for β = 2π. The solution proposed in [14] is to implement the replica idea on the level of form factors.…”

“…The structure of the conserved charge eigenvalues in both cases is very different and so is the kinematical arena [14]. However, in view of (3) the structure of the state space in both theories is very similar as will be shown in section 5, much in the spirit of the replica idea [2,14].…”

“…The physics problem we wish to solve is to construct the "replica-deformed"form factors in the sense of [14] for the SU(2)-invariant massive Thirring model. We shall review some aspects of the replica-deformation in section 2.…”