Spontaneously Broken Spacetime Symmetries and Fermi Liquid Theory

Abstract

I discuss the implications of spontaneously broken spacetime symmetries in context of Condensed Matter Physics (CMP) and High Energy Physics (HEP). Startingwith a minimal set of assumptions, a lot can be learned about complicated many body quantum systems using the ideas from Coset Construction and Eff ective Field theories (EFT). The fact that any symmetry of the full theory must be realized, linearly or non-linearly, in the infra red (IR) limit puts strong constraints on the low energy dynamics of any EFT. In this work, I have mainly focused on the Fermiliquid theory (FLT), which in some sense is the simplest CMP system. Even though the phenomenology of FLT has been worked out extensively, its analysis from thepoint of view of spacetime symmetry breaking has shed some new light on the theory and led to the development of a novel idea the so-called Dynamical Inverse Higgs Mechanism, which is a new way of non-linear realization of broken spacetime symmetries. This technique is developed in this work in great detail. I also worked on a diff erent, yet more intuitive method of understanding broken spacetime symmetries by using the spacetime symmetry algebra. This is related to a well known concept in EFTs, called the Reparametrization Invariance (RPI). I work out several examples of the constraints that arise in HEP EFTs from RPI and how they can also be derived from the symmetry algebra. Lastly in the appendix, I also provide some detailed calculations related to the main body of my thesis anda few other applications of Coset Construction besides Fermi liquids.