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Effects of Non-locality in Gravity and Quantum Theory
- Author / Creator
- Jens Boos
Spacetime—the union of space and time—is both the actor and the stage during physical processes in our fascinating Universe. In Lorentz invariant local theories, the existence of a maximum signalling speed (the “speed of light”) determines a notion of causality in spacetime, distinguishing the past from the future, and the cause from the effect.
This thesis is dedicated to the study of deviations from locality. Focussing on a particular class of non-local theories that is both Lorentz invariant and free of ghosts, we aim to understand the effects of such non-local physics in both gravity and quantum theory. Non-local ghost-free theories are accompanied by a parameter ℓ of dimension length that parametrizes the scale of non-locality, and for that reason we strive to express all effects of non-locality in terms of this symbol. In the limiting case of ℓ = 0 one recovers the local theory, and the effects of non-locality vanish.
In order to address these questions we develop the notion of non-local Green functions, study their causal properties, and demonstrate that non-locality leads to a violation of causality on small scales but may be recovered at macroscopic distances much larger than the scale of non-locality. In particular, we utilize non-local Green functions to construct the stationary gravitational field of point particles and extended bodies in the weak-field limit of non-local gravity and demonstrate explicitly that non-locality regularizes gravitational singularities at the linear level. Boosting these solutions to the speed of light in a suitable limit, we obtain a class of geometries corresponding to non-local regular ultrarelativistic objects.
In the context of quantum mechanics we demonstrate that non-locality affects the scattering coefficients of a scalar field in the presence of a δ-shaped potential: for a critical frequency, the potential becomes completely opaque and reflects 100% of the incoming wave of that frequency. In the realm of non-local quantum field theory we first illustrate that non-locality smoothes the vacuum polarization and thermal fluctuations in the vicinity of a δ-shaped potential and then prove the fluctuation-dissipation theorem in this particular case. Turning towards quantum field theory in curved spacetime, we construct a non-local ghost-free generalization of the Polyakov effective action and evaluate the resulting quantum average of the energy-momentum tensor in the background of a two-dimensional black hole. While non-locality does not affect the asymptotic flux of Hawking radiation in this model, the entropy of the black hole is sensitive to the presence of non-locality. The results presented in this thesis establish several effects of a Lorentz invariant, ghost-free non-locality in the areas of both gravitational and quantum physics.
- Graduation date
- Fall 2020
- Type of Item
- Doctor of Philosophy
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