Toussaint, Vladimir
(2018)
Particle detectors in fermionic and bosonic quantum field theory in flat and curved spacetimes.
PhD thesis, University of Nottingham.
Abstract
This thesis is concerned with aspects of quantum theory of fields in flat and curved spacetimes of arbitrary dimensions along with detecting bosons and fermions on these spacetimes. The thesis is divided into two main parts. In the first part, we analyse an Unruh-DeWitt particle detector that is coupled linearly to the scalar density of a massless Dirac field (neutrino field) in Minkowski spacetimes of dimension d ≥ 2 and on the two-dimensional static Minkowski cylinder, allowing the detector’s motion to remain arbitrary and working to leading order in perturbation theory. In d-dimensional Minkowski spacetime, 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.
In the second part, firstly, we give a thorough discussion for the Bogolubov transformation for Dirac field, and discuss pair creation in a non-stationary spacetime.
Secondly, we derive the in and out vacua Wightman two-point functions for the Dirac field and the Klein-Gordon field for certain class of spatially flat Friedmann-Robertson-Walker (FRW) cosmological spacetimes wherein the two-point functions have the Hadamard form. We then establish the equivalence between the adiabatic vacuum of infinite order and the conformal vacuum in the massless limit. With the field in the conformal Fock vacuum, we then show that the detector’s response to an UDW particle detector coupled linearly to the scalar density of a massless Dirac field in the spatially flat FRW spacetimes in d-dimensions is identical to the response of a detector coupled to the massless scalar field in the spatially flat FRW spacetimes in 2d-dimensions.
Lastly, we discuss a massive scalar field in the spatially compactified (1 + 1)-dimensional FRW spacetime. There, the issue of the conformal zero momentum mode arises. To resolve this issue, we develop a new scheme for quantizing the conformal zero-mode. This new quantization scheme introduces a family of two real parameters for every zero-momentum mode with an associated two-real-parameter set of in/out vacua. We then show that the zero momentum initial state’s wave functional corresponds to a two-real parameter set of Gaussian wave packets. For applications, we examine the finite-time detector’s response to a massive scalar field in the (1 + 1)-dimensional, spatially compactified Milne spacetime. Explicit analytic results are obtained for the comoving and inertially non-comoving trajectories.
Numerical results are provided for the comoving trajectory. The numerical results suggest that when the in-vacuum is chosen to be very far from the conventional Minkowski vacuum state, then it contains particles. As result, spontaneous excitation of the comoving detector occurs.
| Item Type: |
Thesis (University of Nottingham only)
(PhD)
|
| Supervisors: |
Louko, Jorma
Krasnov, K. |
| Keywords: |
Quantum field theory in curved spacetime, nontrivial spacetime, Fermionic zero mode, massive conformal zero mode,
quantum field theory on cosmological spacetimes, Milne universe, particle detectors, response function, Unruh Effect, Hawking radiation |
| Subjects: |
Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter |
| Faculties/Schools: |
UK Campuses > Faculty of Science > School of Mathematical Sciences |
| Item ID: |
49473 |
| Depositing User: |
Toussaint, Vladimir
|
| Date Deposited: |
06 Feb 2018 17:11 |
| Last Modified: |
12 Dec 2021 04:30 |
| URI: |
https://eprints.nottingham.ac.uk/id/eprint/49473 |
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