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AIP conference proceedings

Quantum field theory without Fock space

Roman Sverdlov

Published Jan 1, 2012• 0 citations
Publisher

Abstract

The purpose of this paper is to find a way of encoding the mathematical information of discretized quantum field theory in terms of the ontologically meaningful quantities living in ordinary space.
DOI
10.1063/1.3688986

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The goal of this paper is to re-express QFT in terms of two "classical" fields living in ordinary space with single extra dimension. The role of the first classical field is to set up an injection from the set of values of extra dimension into the set of functions, and then said injection will be used in order to convert the second field into a coarse grained functional, thereby approximating QFT state. It turns out that this work also has a side-benefit of modeling ensemble of states in terms of one single state which, in turn, is interpretted in the above way. It is important to clarify that by "classical" we mean functions over ordinary space rather than configuration, Fock or function space. The "classical" theory that we propose is still non-local.
Ordinary Fock space, defined as concatenated combination of three-dimensional spaces is the main workhorse of the canonical version of quantum field theory. It is also fundamental to the modern version of quantum field theory without observers, as in the theory of Everett, Wheeler and Deutsch, which led to the theory of the universal quantum computer. It also has many practical uses, from quantum optics to the closure of turbulence and the derivation of the emergent behavior of space-time dynamical systems. But many of us believe that time and space are interchangeable to some degree, and that methods based on 4D Fock space are needed. This letter describes two simple mathematical tools to help make that possible. It discusses how computing the emergent statistics of such systems is a proper generalization of value function estimation in machine learning, which may therefore carry the same complexities with it.
We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1. Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2. The Dirac Sea Model3. Equilibrium States and the Vacuum4. Excitations of the Vacuum and the Fock Space Formalism5. The Appearance of Particle Creations and Annihilations6. The Merits of the Bohmian Approach