Covariant canonical quantization of fields and Bohmian mechanics

Abstract

We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard noncovariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional noncovariant WheelerDeWitt approach.

Strings, T-duality breaking, and nonlocality without the shortest distance

“…The Bohmian interpretation has also been proposed as a possible interpretation of noncommutative QM [19]. Using our results on the manifestly covariant canonical quantization of fields [20,21], we have recently argued [22] that the natural formulation of strings compatible with the world-sheet covariance on the quantum level is, indeed, a formulation in terms of Bohmian deterministic hidden variables. All these results suggest that the Bohmian interpretation might provide a more fundamental description of string theory.…”

Strings, world-sheet covariant quantization and Bohmian mechanics

“…However, now comes string theory that saves the situation. If particles are more fundamental than fields, but if they are not really pointlike, but extended objects as in string theory, then the results of [7] can be applied. In this case, the Bohmian interpretation of strings can be derived from the requirement of world-sheet covariance, while the resulting string theory in a pointlike-particle limit reduces to the Bohmian interpretation of relativistic quantum particles.…”

Quantum Mechanics: Myths and Facts

“…(The commutativity of the corresponding variables is provided by the operators σ j ⊗ 1 and 1 ⊗ σ k that correspond to the variables of the first and the second subsystem, respectively.) Instead of (38), consider the state…”

“…In the Bohmian interpretation, this means that Q is the quantum potential which (in the case of entanglement) describes a nonlocal interaction. For attempts to formulate the nonlocal Bohmian interaction in a relativistic covariant way, see, e.g., [34,35,36,37,38,39].…”