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Quantum propagation and initial value problems in curved space. / Ross James Stanley

Swansea University Author: Ross James, Stanley

Abstract

Quantum field theory is studied within the semi-classical gravity approximation. The quantum correction to the propagation of both photons and gravitons in a general curved space background is calculated showing a non-trivial spacetime refractive index as well as a dynamical dressing (or undressing)...

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Published: 2012
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42356
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Abstract: Quantum field theory is studied within the semi-classical gravity approximation. The quantum correction to the propagation of both photons and gravitons in a general curved space background is calculated showing a non-trivial spacetime refractive index as well as a dynamical dressing (or undressing) of the particle state. The initial interacting particle's 'dressing', the cloud of virtual particles that surrounds it, may receive corrections from an infinite number of modes even for flat space. When gravitational tidal effects remove this dressing, squeezing it back into the bare particle, this leads to an amplification in a way consistent with unitarity. There is a possible shift discovered in the graviton wavefront velocity related to higher order curvature couplings, although in this calculation there is also a logarithmic divergence at high frequencies, leading to a breakdown of the perturbative approximation. Next we consider initial value problems and the stability of de Sitter space. Here the self decay of a massive scalar in de Sitter space is proposed to lead to a particle explosion where divergent growth of the field expectation value is observed. Directly investigating this divergent field expectation value a one loop calculation is completed for a massive scalar particle in 3-dimensional de Sitter space. This result has characteristic secular growth that can be summed into a rapidly decaying exponential by using the dynamical renormalisation group. Finally the evolution of two point functions is studied, by numerically solving their equations of motion using the Kaydanoff-Baym equations in 2-dimensional de Sitter space. Here we see a decay of the vacuum state due to the coupling. This appears to be related to the choice of initial conditions be chosen to match the free field vacuum plus non-interacting particles. This choice is made inappropriate by the dynamical dressing of the bare particle states.
Keywords: Theoretical physics.;Quantum physics.
College: College of Science