Misc,
Deterministic models of quantum fields
(December 2005)
Abstract
Deterministic dynamical models are discussed which can be described in
quantum mechanical terms. -- In particular, a local quantum field theory is
presented which is a supersymmetric classical model. The Hilbert space approach
of Koopman and von Neumann is used to study the classical evolution of an
ensemble of such systems. Its Liouville operator is decomposed into two
contributions, with positive and negative spectrum, respectively. The unstable
negative part is eliminated by a constraint on physical states, which is
invariant under the Hamiltonian flow. Thus, choosing suitable variables, the
classical Liouville equation becomes a functional Schroedinger equation of a
genuine quantum field theory. -- We briefly mention an U(1) gauge theory with
``varying alpha'' or dilaton coupling where a corresponding quantized theory
emerges in the phase space approach. It is energy-parity symmetric and,
therefore, a prototype of a model in which the cosmological constant is
protected by a symmetry.
