Alejandro Satz

How often does the Unruh?DeWitt detector click? Regularization by a spatial profile

We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh–DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularized by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero-size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asymptotic behaviour of the transition rate are discussed. A number of stationary and nonstationary trajectories are analysed, recovering in particular the Planckian spectrum for uniform acceleration.

Transition rate of the Unruh-DeWitt detector in curved spacetime

We examine the Unruh–DeWitt particle detector coupled to a scalar field in an arbitrary Hadamard state in four-dimensional curved spacetime. Using smooth switching functions to turn on and off the interaction, we obtain a regulator-free integral formula for the total excitation probability, and we show that an instantaneous transition rate can be recovered in a suitable limit. Previous results in Minkowski space are recovered as a special case. As applications, we consider an inertial detector in the Rindler vacuum and a detector at rest in a static Newtonian gravitational field. Gravitational corrections to decay rates in atomic physics laboratory experiments on the surface of the Earth are estimated to be suppressed by 42 orders of magnitude.

Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?

The transition probability in the first-order perturbation theory for an Unruh-DeWitt detector coupled to a massless scalar field in Minkowski space is calculated. It has been shown recently that the conventional ie regularization prescription for the correlation function leads to non-Lorentz invariant results for the transition rate, and a different regularization, involving spatial smearing of the field, has been advocated to replace it. We show that the non-Lorentz invariance arises solely from the assumption of sudden switch-on and switch-off of the detector, and that when the model includes a smooth switching function the results from the conventional regularization are both finite and Lorentz invariant. The sharp switching limit of the model is also discussed, as well as the fall-off properties of the spectrum for large frequencies.

Black hole entanglement entropy and the renormalization group

We investigate the contributions of quantum fields to black hole entropy by using a cutoff scale at which the theory is described with a Wilsonian effective action. For both free and interacting fields, the total black hole entropy can be partitioned into a contribution derived from the gravitational effective action and a contribution from quantum fluctuations below the cutoff scale. In general the latter includes a quantum contribution to the Noether charge. We analyze whether it is appropriate to identify the rest with horizon entanglement entropy, and find several complications for this interpretation, which are especially problematic for interacting fields.

Semiclassical regime of Regge calculus and spin foams

Abstract Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine—as expected from the semiclassical limit of spin foam models—then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.

Vacuum polarization around stars: Nonlocal approximation

We compute the vacuum polarization associated with quantum massless fields around stars with spherical symmetry. The nonlocal contribution to the vacuum polarization is dominant in the weak field limit and induces quantum corrections to the static exterior metric that depend on the inner structure of the star. It also violates the null energy conditions. We argue that similar results also hold in the low energy limit of quantum gravity. Previous calculations of the vacuum polarization in spherically symmetric spacetimes, based on local approximations, are not adequate for Newtonian stars.

Boundary divergences in vacuum self-energies and quantum field theory in curved spacetime

It is well known that boundary conditions on quantum fields produce divergences in the renormalized energy-momentum tensor near the boundaries. Although irrelevant for the computation of Casimir forces between different bodies, the self-energy couples to gravity, and the divergences may, in principle, generate large gravitational effects. We present an analysis of the problem in the context of quantum field theory in curved spaces. Our model consists of a quantum scalar field coupled to a classical field that, in a certain limit, imposes Dirichlet boundary conditions on the quantum field. We show that the model is renormalizable and that the divergences in the renormalized energy-momentum tensor disappear for sufficiently smooth interfaces.

Analytical result for the vacuum polarization of subtracted rotating black holes

We give an analytical formula for the vacuum polarization of a massless minimally coupled scalar field at the horizon of a rotating black hole with subtracted geometry. This is the first example of an exact, analytical result for a four-dimensional rotating black hole.

On the renormalization of the Gibbons-Hawking boundary term

The bulk (Einstein-Hilbert) and boundary (Gibbons-Hawking) terms in the gravitational action are generally renormalized differently when integrating out quantum fluctuations. The former is affected by nonminimal couplings, while the latter is affected by boundary conditions. We use the heat kernel method to analyze this behavior for a nonminimally coupled scalar field, the Maxwell field, and the graviton field. Allowing for Robin boundary conditions, we examine in which cases the renormalization preserves the ratio of boundary and bulk terms required for the effective action to possess a stationary point. The implications for field theory and black hole entropy computations are discussed.

A new expression for the transition rate of an accelerated particle detector

We analyse the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a quantum field on Minkowski space is regularised by a finite spatial profile. We show, under mild technical assumptions, that the zero size limit of the detector response is well defined, independent of the choice of the profile function, and given by a manifestly finite integral formula that no longer involves epsilon-regulators or limits. Applications to specific trajectories are discussed, recovering in particular the thermal result for uniform acceleration. Extensions of the model to de Sitter space are also considered.