College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

Quantum field theory on a light front has a number of interesting properties. Among these are the vacuum is niavely trivial, spontaneous symmetry breaking must be realized in a very different way than t is realized in instant form quantum field theory, and there are questions about the equivalence of the two approaches.

One of the things that is never addressed in the literature is that the dynamics of free and interacting field theories live on inequivalent Hilbert space representations of the algebra of the fields. My interpretation of this is that the notion of kinematic subgroup, which is central to the meaning of Dirac's forms of dynamics, does not trivially generalize to the field theory case. This talk is an attempt to resolve some issues related to this observation by assuming the existence of a local quantum field theory with all of the expected properties. This avoids issues related to renormalization and rotational covariance.

Using these assumptions I will discuss how kinematic subgroups can be realized, the equivalence of theories with different kinematic subgroups and a consistent treatment of the vacuum and spontaneous symmetry breaking. The path to this from the ``perturbative treatment'' requires tackling the challenging problems of non-perturbative renormalization and rotational covariance which remain open problems.