Group theory and De Sitter QFT - the concept of mass

Master thesis
Research group: 
String Cosmology
Marco Boers

The concept of `mass' has a quite obscure status in de Sitter space. For example, in Minkowski spacetime the absence of a mass term, conformal invariance and light cone propagation are all synonymous, while in de Sitter space this is not the case. In this thesis we investigate whether a group theoretical approach might bring resolvement to this issue. It will be similar to what is done in Minkowski spacetime; the unitary irreducible representation (UIR) spaces of the isometry group are associated with complete sets of one-particle states (elementary systems), and the Casimir operators of the group are associated with the invariants of the quantum-mechanical system (rest mass and spin in Minkowski spacetime). Since the notion `mass' is not well defi ned in de Sitter space, we will consider it in reference to Minkowski spacetime. This reference is inferred by using group contractions. We review a particular (Garidi) mass de finition, given in terms of the parameters labeling the UIRs of the de Sitter isometry group SO(4; 1), and for the scalar field we compare this mass with an alternative defi nition.

Publication date: 
February, 2014