Renormalized Unruh-DeWitt particle detector models for boson and fermion fields

Abstract

Since quantum field theories do not possess proper position observables, Unruh-DeWitt detector models serve as a key theoretical tool for extracting localized spatiotemporal information from quantum fields. Most studies have been limited, however, to Unruh-DeWitt (UDW) detectors that are coupled linearly to a scalar bosonic field. Here, we investigate UDW detector models that probe fermionic as well as bosonic fields through both linear and quadratic couplings. In particular, we present a renormalization method that cures persistent divergencies of prior models. We then show how perturbative calculations with UDW detectors can be streamlined through the use of extended Feynman rules that include localized detector-field interactions. Our findings pave the way for the extension of previous studies of the Unruh and Hawking effects with UDW detectors, and provide new tools for studies in relativistic quantum information, for example, regarding relativistic quantum communication and studies of the entanglement structure of the fermionic vacuum.

Unruh-DeWitt detector’s response to fermions in flat spacetimes

“…This result agrees with the limits, special cases and alternative forms considered in [21,22,23,24]. To set this result in context, recall that the response of an Unruh-DeWitt detector that is linearly coupled to a scalar field in its Minkowski vacuum is [5,7,28] …”

“…Although |Ψ 0 is by assumption Hadamard, formula (2.5) as it stands does not define W (2,2) x(τ ), x(τ ) as a distribution on the detector's worldline because of the partial coincidence limit in (2.5) [21,22,23,24]. To make the response function (2.4) well defined, it will be necessary to give formula (2.5) an appropriate distributional interpretation.…”

“…W (2,2) (x, y) is hence not well defined, due to a divergent additive constant in the second term in (3.16) [21,22,23,24].…”

“…In this paper we consider an Unruh-DeWitt detector coupled to a Dirac field, taking the interaction Hamiltonian to be linear in the Dirac field's scalar density, ψψ [20,21,22,23,24]. The product of ψ and ψ at the same spacetime point makes this interaction more singular than the conventional linear coupling to a scalar field [1,2].…”

“…The product of ψ and ψ at the same spacetime point makes this interaction more singular than the conventional linear coupling to a scalar field [1,2]. Working in linear perturbation theory for a massive Dirac field, the detector's response has a divergent additive term, and although in stationary situations this term been viewed as a formally divergent constant that should be dropped in the dual limit of long interaction and small coupling [21], in nonstationary situations the response would need an additional regularisation, perhaps by a spatial profile or by an appropriate normal ordering [24,25]. In the special case of Minkowski vacuum, the divergent term is however proportional to the mass of the field, and for a massless field a consistent regularisation is accomplished by simply dropping the additive term [22,23].…”