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Bell-type quantum field theories

REVIEW ARTICLE

Detlef Dürr1, Sheldon Goldstein2, Roderich Tumulka3 and Nino Zanghì3

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TOPICAL REVIEW

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 |Ψ|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 processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to 'second quantization'. As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field.


PACS

11.10.Cd Axiomatic approach

02.50.Ga Markov processes

41.20.Jb Electromagnetic wave propagation; radiowave propagation

MSC

60Jxx Markov processes

81T05 Axiomatic quantum field theory; operator algebras

Subjects

Computational physics

Accelerators, beams and electromagnetism

Particle physics and field theory

Dates

Issue 4 (28 January 2005)

Received 20 July 2004, in final form 1 November 2004

Published 12 January 2005



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