Exact uncertainty, bosonic fields, and interacting classical-quantum systems

Abstract

The quantum equations for bosonic fields may be derived using an 'exact uncertainty' approach [1]. This method of quantization can be applied to fields with Hamiltonian functionals that are quadratic in the momentum density, such as the electromagnetic and gravitational fields. The approach, when applied to gravity [2], may be described as a Hamilton-Jacobi quantization of the gravitational field. It differs from previous approaches that take the classical Hamilton-Jacobi equation as their starting point in that it incorporates some new elements, in particular the use of a formalism of ensembles on configuration space and the postulate of an exact uncertainty relation. These provide the fundamental elements needed for the transition to the quantum theory. The formalism of ensembles on configuration space is general enough to describe classical, quantum, and interacting classical-quantum systems in a consistent way. This is of some relevance to gravity: although there are many physical arguments in favour of a quantum theory of gravity, it appears that the justification for such a theory does not follow from logical arguments alone [3]. It is therefore of interest to consider the coupling of quantum fields to a classical gravitational field. This leads to a theory that is fundamentally different from standard semiclassical gravity. 1. Michael J W Hall, Kailash Kumar and Marcel Reginatto, Bosonic field equations from an exact uncertainty principle, J. Phys. A 36 (2003) 9779-9794 (http://arxiv.org/abs/hep-th/0307259). 2. M. Reginatto, Exact Uncertainty Principle and Quantization: Implications for the Gravitational Field, Proceedings of DICE2004 in: Braz. J. Phys. 35 (2005) 476-480 (http://arxiv.org/abs/gr-qc/0501030). 3. Mark Albers, Claus Kiefer and Marcel Reginatto, Measurement analysis and quantum gravity, Phys. Rev. D 78 (2008) 064051 (http://arxiv.org/abs/0802.1978)