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arXiv:hep-th/9807041 · Nuclear Physics B

Varying the Unruh temperature in integrable quantum field theories

Max R. Niedermaier

Published Dec 1, 1998• 11 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(98)00685-3

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Dedicated to the memory of Moshé Flato The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (“replica”) deformation of the form factor approach. We show that replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particle

•Jan 1, 1999•2 citations
Form factor sequences of an integrable QFT can be defined axiomatically as solutions of a system of recursive functional equations, known as "form factor equations". We show that their solution can be replaced with the study of the representation theory of a novel algebra F(S). It is associated with a given two-particle S-matrix and has the following features: (i) It contains a double TTS algebra as a subalgebra. (ii) Form factors arise as thermal vector states over F(S) of temperature 1=2ß. The thermal ground states are in correspondence to the local operators of the QFT. (iii) The underlying `finite temperature structure' is indirectly related to the "Unruh effect" in Rindler spacetime. In F(S) it is manifest through modular structures (j; ffi) in the sense of algebraic QFT, which can be implemented explicitly in terms of the TTS generators. 1. Introduction and survey The form factor approach to integrable quantum field theories (QFTs) has several remarkable features. First it yiel...
Using the Schwinger-Keldysh path integral, we draw a connection between localized quantum field theories and more commonly used models of local probes in relativistic quantum information (RQI). By integrating over and then tracing out the inaccessible modes of the localized field being used as a probe, we show that, at leading order in perturbation theory, the dynamics of any finite number of modes of the probe field is exactly that of a finite number of harmonic-oscillator Unruh-DeWitt (UDW) detectors. The equivalence is valid for a rather general class of input states of the probe-target field system, as well as for any arbitrary number of modes included as detectors. The path integral also provides a closed-form expression which gives us a systematic way of obtaining the corrections to the UDW model at higher orders in perturbation theory due to the existence of the additional modes that have been traced out. This approach vindicates and extends a recently proposed bridge between detector-based and field-theory-based measurement frameworks for quantum field theory [T. R. Perche et al., Particle detectors from localized quantum field theories, Phys. Rev. D 109, 045013 (2024).], and also points to potential connections between particle detector models in RQI and other areas of physics where path integral methods are more commonplace---in particular, the Wilsonian approach to the renormalization group and effective field theories.
Dedicated to the memory of Moshé Flato The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (“replica”) deformation of the form factor approach. We show that replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particle