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

Louko, Jorma; Toussaint, Vladimir

Authors

Vladimir Toussaint



Abstract

We examine an Unruh-DeWitt particle detector that is coupled linearly to the scalar density of a massless Dirac field in Minkowski spacetimes of dimension d≥2 and on the static Minkowski cylinder in spacetime dimension two, allowing the detector’s motion to remain arbitrary and working to leading order in perturbation theory. In d -dimensional Minkowski, with the field in the usual Fock vacuum, we show that the detector’s response is identical to that of a detector coupled linearly to a massless scalar field in 2d -dimensional Minkowski. In the special case of uniform linear acceleration, the detector’s response hence exhibits the Unruh effect with a Planckian factor in both even and odd dimensions, in contrast to the Rindler power spectrum of the Dirac field, which has a Planckian factor for odd d but a Fermi-Dirac factor for even d . On the two-dimensional cylinder, we set the oscillator modes in the usual Fock vacuum but allow an arbitrary state for the zero mode of the periodic spinor. We show that the detector’s response distinguishes the periodic and antiperiodic spin structures, and the zero mode of the periodic spinor contributes to the response by a state-dependent but well-defined amount. Explicit analytic and numerical results on the cylinder are obtained for inertial and uniformly accelerated trajectories, recovering the d=2 Minkowski results in the limit of large circumference. The detector’s response has no infrared ambiguity for d=2 , neither in Minkowski nor on the cylinder.

Citation

Louko, J., & Toussaint, V. (2016). Unruh-DeWitt detector’s response to fermions in flat spacetimes. Physical Review D, 94(6), https://doi.org/10.1103/PhysRevD.94.064027

Journal Article Type Article
Acceptance Date Aug 20, 2016
Publication Date Sep 9, 2016
Deposit Date Jul 7, 2017
Publicly Available Date Jul 7, 2017
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 94
Issue 6
Article Number 064027
DOI https://doi.org/10.1103/PhysRevD.94.064027
Keywords Quantum fields in curved space time, Unruh effect, Gravitation
Public URL http://eprints.nottingham.ac.uk/id/eprint/44054
Publisher URL https://doi.org/10.1103/PhysRevD.94.064027
Related Public URLs https://arxiv.org/abs/1608.01002
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information ©2017 American Physical Society

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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