The Unruh-DeWitt model and its joint interacting Hilbert space
- Author(s)
- Erickson Tjoa, Finnian Gray
- Abstract
In this work we make the connection between the Unruh-DeWitt (UDW) particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson (SB) model. With some modifications, we show that existing results about the existence of a SB ground state can be adapted to the UDW model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the UDW model describes a simplified model of light-matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared (IR) divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications.Our work clarifies the connection between obstructions due to Haag’s theorem and IR bosons in the SB models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.
- Organisation(s)
- Gravitational Physics
- External organisation(s)
- Max-Planck-Institute of Quantum Optics
- Journal
- Journal of Physics A: Mathematical and Theoretical
- Volume
- 57
- No. of pages
- 45
- ISSN
- 1751-8113
- DOI
- https://doi.org/10.48550/arXiv.2402.05795
- Publication date
- 08-2024
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103024 Quantum field theory, 103028 Theory of relativity, 103012 High energy physics
- Keywords
- ASJC Scopus subject areas
- Statistical and Nonlinear Physics, Statistics and Probability, Modelling and Simulation, Mathematical Physics, Physics and Astronomy(all)
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/the-unruhdewitt-model-and-its-joint-interacting-hilbert-space(4e956d35-47fe-462f-828a-01295f301e70).html