The Effect of Tunnelling in Quantum Field Theory

The phenomenon of quantum tunnelling is a familiar one, allowing a particle to ‘escape’ from a potential well where it does not have enough energy classically to penetrate the potential barrier. Quantum tunnelling is well studied and familiar to most physicists from processes such as alpha decay. In this thesis we will examine the phenomenon of tunnelling in Quantum Field Theory which will yield a rich phenomenology. In the strong and electroweak sectors it gives rise to the instanton, a field configuration which tunnels between degenerate minima of the field strength. In the strong sector we will compute the cross section for these processes at hadron colliders before examining potential search strategies. In the electroweak sector we will show that such processes are always exponentially suppressed and hence unobservable at any present or future colliders. Finally we will look at the phenomenon of tunnelling in the early universe in the context of first-order phase transitions; here tunnelling can lead to the production of gravitational waves which could be observable at future gravitational wave detectors, and models giving rise to such signals can also be used to solve other shortcomings of the Standard Model such as the hierarchy problem and the absence of dark matter.