THE DEBROGLIE-BOHM THEORY OF MOTION AND QUANTUM-FIELD THEORY

De Broglie and Bohm successfully showed how the statistical phenomena of nonrelativistic quantum mechanics could be understood as the outcome of individually well defined processes in which physical systems have a corpuscular aspect that pursues a spacetime track. A review is presented of the application of the de Broglie-Bohm method to relativistic boson systems. After summarizing the salient points of the nonrelativistic theory, it is explained why a trajectory interpretation of the Klein-Gordon equation is in general untenable. Then a consistent version of the approach that takes fields as basic variables is presented following a previous analysis based on Bohm's original work. All the formulae needed to apply the theory in the space and normal coordinate representations are given and illustrated through applications to the ground state, the Casimir effect, the number and coherent states, and the classical limit. Emphasis is laid on the nonlocality and noncovariance of the individual processes that underlie the statistical locality and Lorentz covariance of quantum field theory in its canonical formulation. Particular attention is paid to the question of whether it is possible to attribute spacetime trajectories to the quanta of the bosonic field. It is found that this is not possible if the current field-theoretic formalism is adopted unmodified. As an alternative the notion of energy flow lines is investigated and shown to be consistent in classical optics, but only for certain states in quantum optics. The field and energy guidance laws are applied to two-slit interference experiments performed with number and coherent states. Finally, the value of this approach is illustrated through the light it sheds on the problem of interpreting the wavefunction of the universe.