A quantum field theory as emergent description of constrained supersymmetric classical dynamics
Abstract
Description
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 evolution of an ensemble of such classical systems. With the help of the supersymmetry algebra, the corresponding Liouville operator can be 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. In this way, choosing suitable phase space coordinates, the classical Liouville equation becomes a functional Schroedinger equation of a genuine quantum field theory. Quantization here is intimately related to the constraint, which selects the part of Hilbert space where the Hamilton operator is positive. This is interpreted as dynamical symmetry breaking in an extended model, introducing a mass scale which discriminates classical dynamics beneath from emergent quantum mechanical behaviour.
17 pages. Based on talks at Path Integrals 2005 - ``From Quantum Information to Cosmology'' (Prague), Quantum Physics of Nature 2005 (Vienna), and Convegno Informale di Fisica Teorica - Cortona 2005; to appear in the proceedings
17 pages. Based on talks at Path Integrals 2005 - ``From Quantum Information to Cosmology'' (Prague), Quantum Physics of Nature 2005 (Vienna), and Convegno Informale di Fisica Teorica - Cortona 2005; to appear in the proceedings