Abstract. 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 numbers: 03.65.Ta, 02.50.−r, 03.70.+k

Print publication: Issue 4 (28 January 2005)
Received 20 July 2004, in final form 1 November 2004
Published 12 January 2005