Entropic dynamics: reconstructing quantum field theory in curved space-time

Abstract

The Entropic Dynamics reconstruction of quantum mechanics is extended to the quantum theory of scalar fields in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kuchař, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest relations for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.

An Entropic Dynamics Approach to Geometrodynamics

“…Whatever the choice of canonical variables, or whether the background is fixed or dynamical, the same "algebra" must hold. As one might expect, the ED formulated here with a dynamical background shares some similarities with the theory developed in [7] [8], in the context of a fixed background. Most obvious is that the variables ρ and φ, or equivalently, ρ and Φ remain canonically conjugate, forming the socalled ensemble phase space, or e-phase space for short.…”

“…(For additional details on entropic time, see e.g., [3].) Here we introduce a manifestly covariant notion of entropic time, along the lines of that in [7] [8].…”

“…(14) similarly decomposing into ensemble and gravitational pieces so that each can be solved independently of the other. The appropriate super-momentum for the ensemble sector was given in [7] [8], with the result that…”

“…That is, the gravitational side can proceed as if there were no sources, while the matter side can proceed along lines similar to [7] [8].…”

“…But we also wish to proceed conservatively; our aim is not,after all, to simply discard information which has already been proven valuable in ED. Thus we proceed in a minimalist fashion by taking the constraints of [7] [8] and altering them to account for the additional information; which amounts here to a different choice of variables to describe the geometry. Following the seminal work of Hojman, Kuchař, and Teitelboim in [11], we make a choice in which the metric of three-dimensional space is itself a canonical variable.…”