Geometro-stochastic quantization of massive fields in curved space-time

Abstract

It is shown that an earlier introduced concept of quantum geometry, given by a Hilbert bundle over a base space whose elements constitute a generic curved space-time and represent the mean locations of quantum frames, can be generalized to the case of Fock bundles, whose Fock fibres are the carriers of multiparticle states. In this new context, the role of quantum Lorentz frame is taken over by second-quantized frames constructed out of coherent exciton states. The structure groups of the considered bundles contain unitary representations of the Poincare group, with the latter emerging as a gauge group for the internal degrees of freedom of the considered quantum particles. Connections compatible with the Hermitian structure are introduced on bundles of second-quantized frames that are associated to principal bundles of affine Lorentz frames. The corresponding parallel transport is expressed in terms of path integrals for quantum frame propagators. It is shown that the resulting geometro-stochastic quantum field theory in curved space-time does not give rise to the foundational difficulties with the particle concept, with normal ordering and with the definition of the stress-energy tensor, that are inherent in more conventional approaches to quantum field theory in curved space-time. Hence, the derived path integral formulae for the propagation of systems of quantum field particles display in the present framework none of the ambiguities encountered by those approaches.