Bohmian Mechanics and Quantum Field Theory

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.

Figure 1

Two patterns of world lines as they may arise from some Bell-type QFT. (a) The world line of a photon (dashed curve) starts at an emission event (at time $t_1$) on the world line of an electron (solid curve) and ends at an absorption event (at time $t_2$) on the world line of another electron. (b) An electron-positron pair (solid curves) is created at the end point of a photon world line.

Figure 2

Schematic representation of the configuration space of a variable number of particles. (a)–(d) show the sectors ${\mathcal{Q}}^{[0]}$ through ${\mathcal{Q}}^{[3]}$. A configurational history $Q(t)$ jumps to the next higher sector at each creation event and to the next lower sector at each annihilation event. The history shown corresponds to a world line pattern such as that of Fig. 1a.