Dissertation

Algebraic Formulation of the Light-Front Vacuum

Herrmann, Marc

2020

Overview

In the light-front formulation of quantum field theory, one finds that the vacuum of an interacting theory has a very simple relationship to the vacuum of a free theory. This relationship is not present in the equal-time formulation. In order to further explore this property, we can use the framework of algebraic quantum field theory. In this framework there are two central ingredients. First, there is a C*-algebra corresponding to the collection of possible observables. Second, there is a positive linear functional acting on the algebra which assigns to each element of the algebra, the vacuum expectation value of that element. This framework is applied to a simplified model of two massive scalar fields each with a different mass. In this context, the triviality of the light-front vacuum can be studied by considering the equivalence between representations of the canonical commutation relations associated with each free field. Using the original description of the light-front C*-algebra, first proposed by Leutwyler, Klauder, and Streit, these representations can be shown to be unitar- ily equivalent. However, in order to ensure that the resulting representations satisfy the properties of a local quantum theory, the light-front algebra needs to be modified in such a way that the description of the algebra is dependent on the mass of the field. As a result, the representations associated with each free field are no longer unitarily equivalent. They are instead quasi-equivalent. This property is shared by the equal-time representations as well. In this way we are able to restore some degree of similarity between the light-front and equal-time descriptions of the vacuum, and lay the groundwork for developing a deeper understanding the light-front vacuum.

• Publisher: ProQuest Dissertations & Theses
• Subject: Mathematics / Quantum physics / Theoretical Mathematics / Theoretical physics
• ISBN: 9798672163000