Quantum field theory on a seven-dimensional homogeneous space of the Poincaré group

Abstract

Field theories over the homogeneous space of the Poincaré group consisting of the direct product of ordinary Minkowski space M and a three-dimensional timelike hyperboloid H3 are investigated in an effort to provide a description of a relativistic extended body. The locality properties of such fields are investigated, and it is found that such fields are in general nonlocal with the nonlocal behavior governed by the type of representations used. It is also found that an internal O(4) symmetry arises quite naturally and is used to construct a model describing an infinite number of particles with an almost linear mass spectrum. This model provides no unphysical solutions, decreasing electromagnetic vertex functions, positive definite field energy, and weak nonlocality. All the vertex functions are calculated and discussed.