College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

I have long been puzzled as to why the fundamental theory of relativistic quantum mechanics is a field theory and not a particle theory. In this talk I give several reasons standing in the way of a relativistic particle theory. Starting with the irreps of the Poincare group, I then formulate a particle theory in terms of bare creation and annihilation operators rather than field operators, after specifying the equations such a theory must satisfy, I introduce operators that give meaning to the localization of particles.

Scattering is formulated using ideas from a paper of Eckstein and applied to non relativistic scattering. Two applications of the formalism are presented, one involving the renormalization of the self interaction of a scalar meson, the other a vertex interaction of a charged meson with an uncharged meson.