Scalar propagator for planar gravitational waves

Abstract

We construct the massive scalar propagator for planar gravitational wave backgrounds propagating on Minkowski space. We represent the propagator in terms of the Bessel's function of suitably deformed nonlocal distance functions, the deformation being caused by gravitational waves. We calculate the propagator both for nonpolarized, for the plus (+) and cross (×) polarized plane waves, as well as for more general planar waves in D spacetime dimensions. The propagator is useful for studying interactions of scalar fields on planar gravitational wave backgrounds in the context of interacting quantum fields, in which renormalization plays a crucial role. As simple applications of the propagator we calculate the one-loop effective action, the scalar mass generated by the scalar self-interaction term and the one-loop energy-momentum tensor, all renormalized by using dimensional regularization and renormalization. While the effective action and scalar mass remain unaffected by gravitational waves, the energy-momentum tensor exhibits flow of energy density in the direction of gravitational waves which grows quadratically with the scalar field mass, gravitational wave amplitude and its frequency.

Gravitational wave signals in an Unruh-de Witt detector

“…In this work we calculate the response of a freely falling Unruh-de Witt detector which couples to massless or massive scalar field fluctuating in the presence of planar gravitational waves propagating on Minkowski spacetime. This work builds on earlier studies [2,3,4,7,8,9,1], which address some aspects of the problem of how planar gravitational waves affect scalar fields. In particular the authors of Ref.…”

“…In this work we generalize the monochromatic wave background considered in Ref. [1] to the case when the gravitational wave strain, h ij = h ij (u), is characterised by a general function of u propagating in the x D−1 direction. Motivated by the form of gravitational waves emitted by realistic sources, whose wave form can be decomposed into the fundamental mode of frequency ω g , and the higher overtones (whose frequencies are nω g ), we shall consider gravitational waves of the form, (1.4) where h…”

“…These integrals can be performed by a straightforward generalization of the method presented in Appendices A and B of Ref. [1] (see also Appendix A of this work), resulting in,…”

“…In this work we generalize their analysis by using the propagator recently obtained in Ref. [1]. For simplicity, we do not analyse here the response of the detector moving along noninertial trajectories.…”

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We firstly generalize the massive scalar propagator for gravitational waves propagating on Minkowski space obtained recently in Ref. [1]. We then use this propagator to study the response of a freely falling Unruh-de Witt detector to a gravitational wave backg round.

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