Deterministic models of quantum fields

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 [1]. 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 Schrödinger 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 [2]. It is energy-parity symmetric and, therefore, a prototype of a model in which the cosmological constant is protected by a symmetry.

A Path Integral for Classical Dynamics, Entanglement, and Jaynes-Cummings Model at the Quantum-Classical Divide

“…The close relation between classical and quantum mechanical dynamics that we uncovered may help to address in new ways problems related to the nature of classical or quantum states, 26,28,29 to the pathways, if any, over the quantum-classical divide, 1,2,4,5,9 or the measurement problem. 3,7 …”

“…5,29 Presently, we have concentrated on the similarities and di®erences between both evolution equations.…”

“…Field theories require a classical functional formalism. 5,18 Furthermore, the Eq. (5) appears as the von Neumann equation for a density operatorðtÞ, considering ðQ; q; tÞ as its matrix elements.…”

Ricci Flow, Quantum Mechanics and Gravity

“…In this spirit one should also cite [14,15], where it has been speculated that gravity could possibly have a quantum origin. Further interesting topics at the interface of gravity and quantum mechanics are dealt with in [16][17][18][19][20][21][22]; a classical/quantum duality with gravitational side effects has been analyzed in [23][24][25]. Other issues, in principle outside the realm of quantum gravity and concerning quantum mechanics proper, but in fact intimately related, are interpretational problems such as the measurement problem and the collapse of the wavefunction [26].…”

A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

“…Part of the motivation for the present work comes from recent considerations of the possibility of a deterministic foundation of quantum mechanics, as it has already been verified in a number of models [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. While general principles and physical mechanisms ruling the construction of a deterministic classical model underlying a given quantum field theory are hard to come by, cf.…”