# Bell-type quantum field theories

@article{Duerr2004BelltypeQF, title={Bell-type quantum field theories}, author={Detlef Duerr and Sheldon Goldstein and Roderich Tumulka and Nino Zangh{\'i}}, journal={Journal of Physics A}, year={2004}, volume={38} }

In his paper (1986 Beables for quantum field theory Phys. Rep. 137 49?54) John S Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |?|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; we call such processes Bell-type quantum field theories. We describe methods for explicitly constructing these…

## 92 Citations

Stochasticity and Bell-type quantum field theory

- Computer Science, MathematicsSynthese
- 2018

This paper critically discusses an objection proposed by Nikolić against the naturalness of the stochastic dynamics implemented by the Bell-type quantum field theory, an extension of Bohmian…

A Persistent Particle Ontology for Quantum Field Theory in Terms of the Dirac Sea

- PhysicsThe British Journal for the Philosophy of Science
- 2019

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…

Pilot-wave approaches to quantum field theory

- Physics
- 2011

The purpose of this paper is to present an overview of recent work on pilot-wave approaches to quantum field theory. In such approaches, systems are not only described by their wave function, as in…

Bohmian mechanics and quantum field theory.

- Physics, MedicinePhysical review letters
- 2004

A recently proposed extension of Bohmian mechanics to quantum field theory is discussed, which describes explicit creation and annihilation events of particles: the world lines for the particles can begin and end.

The Analogue of Bohm-Bell Processes on a Graph

- Physics
- 2006

Abstract Bohm–Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes Q t generalizing in a natural way both Bohm's dynamical system in configuration…

Quantum Hamiltonians and Stochastic Jumps

- Mathematics, Physics
- 2005

With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics.…

Bohmian Quantum Gravity and Cosmology

- PhysicsApplied Bohmian Mechanics
- 2019

Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical…

Some Jump Processes in Quantum Field Theory

- Mathematics, Physics
- 2005

A jump process for the positions of interacting quantum particles on a lattice, with time-dependent transition rates governed by the state vector, was first considered by J.S. Bell. We review this…

Pilot Wave Theory and Quantum Fields

- Physics
- 2011

Pilot wave theory (PWT), also called de Broglie-Bohm theory or Bohmian Mechanics, is a deterministic nonlocal `hidden variables' quantum theory without fundamental uncertainty. It is in agreement…

A minimalist pilot-wave model for quantum electrodynamics

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2007

We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic and not to the fermionic degrees of freedom of the…

## References

SHOWING 1-10 OF 46 REFERENCES

Generalized beable quantum field theory

- Physics
- 1990

Abstract Generalising the Broglie-Bohm quantum mechanics without wave-function collapse, Bell formulated the “beable quantum field theory”. The local beables n ( t ) exist independent of observation…

Quantum Hamiltonians and Stochastic Jumps

- Mathematics, Physics
- 2005

With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics.…

Global Existence of Bell's Time-Inhomogeneous Jump Process for Lattice Quantum Field Theory

- Mathematics, Physics
- 2004

We consider the time-inhomogeneous Markovian jump process in- troduced by John S. Bell (4) for a lattice quantum field theory, which runs on the associated configuration space. Its jump rates,…

Quantum equilibrium and the origin of absolute uncertainty

- Mathematics, Physics
- 1992

The quantum formalism is a “measurement” formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from…

Objective interpretations of quantum mechanics and the possibility of a deterministic limit

- Physics
- 1987

Examines a suggestion by Bell (1984) that a deterministic model might be furnished by the continuum limit of an objective stochastic model which he has proposed for quantum field theory on a lattice.…

Quantum mechanics in terms of discrete beables.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1993

An interpretation of quantum mechanics in terms of classical concepts, «beables,» due to de Broglie, Bohm, and Bell (BBB) is generalized and further developed and it is shown that, in the continuum limit, this interpretation reduces to the causal one of Bohm.

Stochastic processes of a quantum state

- Mathematics
- 1985

Starting from a quantum state represented by its wave function Ψ(x), satisfying the Schrödinger equation, we determine stochastic processes which provide the same time evolution for the probability…

Local quantum physics : fields, particles, algebras

- Physics
- 1993

This textbook gives a comprehensive account of local quantum physics understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach, it describes…

Naive Realism about Operators

- Mathematics, Physics
- 1996

A source of much difficulty and confusion in the interpretation of quantum mechanics is a “naive realism about operators.” By this we refer to various ways of taking too seriously the notion of…

A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II

- Physics
- 1952

In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of hidden variables developed in a…