AbstractIn this thesis we investigate the effects of low-order quantum corrections on
Lifshitz-type quantum field theories. In particular, we consider the Lorentz-symmetry violating corrections to the dispersion relations of the various particles of these theories at low energies, which may be of a significant size even where the classical effect is small.
We first study a Lifshitz scaling model of two fermion flavours in flat at space,
interacting by a flavour mixing four-point term. We demonstrate the dynamical
generation of masses and flavour oscillations and consider these as a possible model of neutrino mixing. We use existing experimental constraints on neutrino masses and mixing angles to place restrictions on the couplings of our model. We then investigate quantum corrections to the couplings and dispersions, and finnd that the latter would be too large to be considered physical.
Next, we investigate a Lifshitz scaling model of Quantum Electrodynamics, containing only fermions and gauge fields. We investigate the extent to which such models may be phenomenologically viable, again primarily through calculating low-order dressed dispersion relations. In doing this, we encounter issues not seen in the simpler model such as those of gauge fixing and dimensional regularisation in anisotropic theories. We again finnd that the dressed dispersion relations appear notably non-relativistic even at low energies, despite the classical model being well within experimental bounds.
Finally, we investigate the dressing of scalar and vector boson dispersion relations by the quantum effects of the so-called 'covariant' extension of Horava-Lifshitz gravity, which despite having an unusual extra symmetry seems better behaved than the 'original' form of Horava gravity. We find that even integrating out the effects of quantum gravity fluctuations alone gives significant corrections to the matter sector's dispersion relations, which allows us to place some new constraints on the energy scales of the theory.
|Date of Award
|Jean Alexandre (Supervisor) & Bobby Acharya (Supervisor)