The Unruh-DeWitt model and its joint interacting Hilbert space
arxiv(2024)
摘要
In this work we make the connection between the Unruh-DeWitt particle
detector model applied to quantum field theory in curved spacetimes and the
rigorous construction of the spin-boson model. With some modifications, we show
that existing results about the existence of a spin-boson ground state can be
adapted to the Unruh-DeWitt model. In the most relevant scenario involving
massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes,
where the Unruh-DeWitt 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
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.
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