Non-Hermitian quantum field theory

Abstract

The main objective of this thesis is to provide a better understanding of non- Hermitian, PT-symmetric Quantum Field Theories. In particular we focus on a non-Hermitian extension of the scalar sector of the Standard Model. Firstly, we consider a non-Hermitian Lagrangian that consists out of two complex scalar fields. We discuss a consistent manner to define the equations of motion and we reexamine the relation between transformations and conserved currents. Because of the non-Hermitian behaviour of our system the relation between conserved currents and symmetries, known as the Noether’s theorem, no longer holds. We later discuss spontaneous symmetry breaking of our scalar model and show that the Goldstone theorem still applies for our non-Hermitian scalar model. We show that the Goldstone theorem relies on the existence of a conserved current, whose transformation breaks the vacuum. As discussed before, this transformation will not be a symmetry of our system. Additionally, we show how the conventional quantisation of the path integral formulation should be extended consistently for PT-symmetric, non-Hermitian systems. Secondly, we include an Abelian gauge field into our theory. Ensuring Gauge invariance is nontrivial for this model. We dicuss the problems that occur and propose a method to build a consistent theory. We then discuss a non-Hermitian extension to the Englerd-Brout-Higgs mechanism for mass generating of the gauge field. Finally, we also include non-Abelian SU(2) gauge fields and naturally end up with a non-Hermitian two-Higgs-doublet model extension to the Standard Model. We then compare its mass spectrum to that of a Hermitian two-Higgs-doublet model.

Date of Award	1 Dec 2020
Original language	English
Awarding Institution	King's College London
Supervisor	Jean Alexandre (Supervisor)