SO(4,1)-Coherent states and the geometro-stochastic quantization of a gauge theory for extended objects

Abstract

Coherent states associated with the principal series of unitary irreducible representations of the (4,1)-de Sitter group are considered for the use in a stochastically quantized gauge theory defined on a Hilbert bundle over curved space-time carrying a phase space representation of SO(4,1). The bundle geometry is characterized by a fundamental length parameter R taken to be of a size typical for hadron physics.