Parametrizing Fluids in Canonical Quantum Gravity

Abstract

The problem of time is an unsolved issue of canonical General Relativity. A possible solution is the Brown-Kuchař mechanism which couples matter to the gravitational field and recovers a physical, i.e. non vanishing, observable Hamiltonian functional by manipulating the set of constraints. Two cases are analyzed. A generalized scalar fluid model provides an evolutionary picture, but only in a singular case. The Schutz' model provides an interesting singularity free result: the entropy per baryon enters the definition of the physical Hamiltonian. Moreover in the co-moving frame one is able to identify the time variable τ with the logarithm of entropy.

Quantum gravity corrections to the matter dynamics in the presence of a reference fluid

“…which is a functional equation, with the same form as the Schrödinger one, when one defines the quantum clock of the theory with the time derivative as above. We remark that definition ( 42) is a generalization of the time derivative implemented in the Kuchař-Torre model when choosing the time parameter as exactly the Gaussian time (15); however, we here maintain the Gaussian coordinates as functions of the generalized parameters, thus we do not need to implement a specific coordinate choice with this definition. We also point out that it is possible to implement a simplified form of the time derivative by using the supermomentum constraint (23), since it takes away a term from the right-hand side.…”

“…the absence of a time evolution of the Universe wavefunction [8][9][10][11]. This basic problem of the quantum gravitational field dynamics has been faced in literature by many approaches, some dealing with the Schrödinger equation [12][13][14][15][16][17][18], and others facing related topics [19][20][21][22][23][24], although this problem still remains an open issue, especially for what concerns the definition of a causality relation.…”

“…A recurring proposal has been to somehow define time via fluid variables into the theory, such as in [12,13,15,27]. In this context, a very interesting attempt must be considered the analysis in [12], where the request to constrain the canonical procedure to a specific Gaussian reference frame has been pursued in a covariant formulation.…”

Quantum gravity corrections to the matter dynamics in the presence of a reference fluid

“…One of the most puzzling questions affecting the canonical quantization [1] of the gravitational field [2][3][4][5][6][7] is the socalled "frozen formalism," i.e., the absence of a time evolution of the Universe wave function [8][9][10][11]. This basic problem of the quantum gravitational field dynamics has been faced in the literature by many approaches, some dealing with the Schrödinger equation [12][13][14][15][16][17][18] and others facing related topics [19][20][21][22][23][24], although this problem still remains an open issue, especially for what concerns the definition of a causality relation.…”

“…A recurring proposal has been to somehow define time via fluid variables into the theory, such as in [12,13,15,27,28]. In this context, a very interesting attempt must be considered in the analysis in [12], where the request to constrain the canonical procedure to a specific Gaussian reference frame has been pursued in a covariant formulation.…”