Mathematical Physics Seminar
By using the light-front formulation of quantum field theory, one can construct a relatively simple relationship between the vacuum of an interacting theory and the vacuum of a free theory. In the usual formulation, this relationship becomes problematic as a result of incorporating the infinite number of canonical variables required for a field theory. We’ll discuss a simple model, based on the coherent states of a harmonic oscillator, which clarifies how the light-front formulation can get around these difficulties.
To further explain the unusual behavior of the light-front vacuum, we can use the techniques of algebraic quantum field theory. In this setup, the theory is constructed from just two ingredients, a $C^*$-algebra constructed from the possible observables of the theory, and positive linear functional corresponding to the vacuum vector.