Constructing point form mass operators from vertex interactions

Abstract

A relativistic few-body theory is formulated using point form quantum mechanics, in which all of the interactions are in the four-momentum operator and Lorentz transformations are kinematic. The four-momentum operator is written as a product of mass and four-velocity operators, where the mass operator is the sum of free and interacting mass operators. Interacting mass operators are constructed from vertices, products of local field operators, evaluated at the space–time point zero. Matrix elements of such mass operators, evaluated on four-velocity eigenstates of a truncated Fock space, which is the space of the few-body theory, are shown to behave like relativistic potentials. Examples for a simple vertex are given.