Bell-type quantum field theories

Abstract

In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate\nparticle trajectories with a lattice quantum field theory, yielding what can be\nregarded as a |Psi|^2-distributed Markov process on the appropriate\nconfiguration space. A similar process can be defined in the continuum, for\nmore or less any regularized quantum field theory; such processes we call\nBell-type quantum field theories. We describe methods for explicitly\nconstructing these processes. These concern, in addition to the definition of\nthe Markov processes, the efficient calculation of jump rates, how to obtain\nthe process from the processes corresponding to the free and interaction\nHamiltonian alone, and how to obtain the free process from the free Hamiltonian\nor, alternatively, from the one-particle process by a construction analogous to\n"second quantization." As an example, we consider the process for a second\nquantized Dirac field in an external electromagnetic field.\n