scholarly journals Quantum geometrodynamics of Einstein and conformal (Weyl-squared) gravity

2017 ◽  
Vol 880 ◽  
pp. 012002
Author(s):  
Claus Kiefer ◽  
Branislav Nikolić
Keyword(s):  
Quantum Geometrodynamics

scholarly journals CONSTRAINTS IN QUANTUM GEOMETRODYNAMICS

2004 ◽  
Vol 19 (10) ◽  
pp. 1609-1638 ◽  
Author(s):  
ADRIAN P. GENTLE ◽  
NATHAN D. GEORGE ◽  
ARKADY KHEYFETS ◽  
WARNER A. MILLER
Keyword(s):  
Quantum Gravity ◽  
General Setting ◽  
Square Root ◽  
Dynamical Equations ◽  
Dynamic Content ◽  
Quantization Formalism ◽  
Canonical Quantum Gravity ◽  
First Time ◽  
Quantum Geometrodynamics ◽  
Canonical Quantum

We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3-geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies.

scholarly journals REVISED CANONICAL QUANTUM GRAVITY VIA THE FRAME FIXING

2004 ◽  
Vol 13 (01) ◽  
pp. 165-186 ◽  
Author(s):  
SIMONE MERCURI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Dynamics ◽  
Fundamental Problem ◽  
Semiclassical Limit ◽  
Momentum Density ◽  
Hamiltonian Constraint ◽  
Additional Energy ◽  
Canonical Quantum Gravity ◽  
Quantum Geometrodynamics ◽  
Canonical Quantum ◽  
Natural Way

We present a new reformulation of the canonical quantum geometrodynamics, which allows one to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the restated dynamics. More precisely, to remove the ambiguity contained in the Wheeler–DeWitt approach, with respect to the possibility of a (3+1)-splitting when space–time is in a quantum regime, we fix the reference frame (i.e. the lapse function and the shift vector) by introducing the so-called kinematical action. As a consequence the new super-Hamiltonian constraint becomes a parabolic one and we arrive to a Schrödinger-like approach for the quantum dynamics. In the semiclassical limit our theory provides General Relativity in the presence of an additional energy–momentum density contribution coming from non-zero eigenvalues of the Hamiltonian constraints. The interpretation of these new contributions comes out in natural way that soon as it is recognized that the kinematical action can be recasted in such a way that it describes a pressureless, but, in general, non-geodesic perfect fluid.

scholarly journals Quantum geometrodynamics of the Bianchi IX cosmological model

2006 ◽  
Vol 23 (13) ◽  
pp. 4333-4351 ◽  
Author(s):  
Arkady Kheyfets ◽  
Warner A Miller ◽  
Ruslan Vaulin
Keyword(s):  
Cosmological Model ◽  
Bianchi Ix ◽  
Quantum Geometrodynamics

scholarly journals QUANTUM GEOMETRODYNAMICS OF THE BIANCHI-IX MODEL IN EXTENDED PHASE SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4473-4490 ◽  
Author(s):  
V. A. SAVCHENKO ◽  
T. P. SHESTAKOVA ◽  
G. M. VERESHKOV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Invariant Solution ◽  
Closed Universe ◽  
Extended Phase ◽  
Probability Interpretation ◽  
Bianchi Ix ◽  
The Universe ◽  
Quantum Geometrodynamics ◽  
Standard Probability

A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noninvariant and thus consistent with the observation conditions of a closed universe, by that being considerably distinguished from the traditional Wheeler–DeWitt one. For the Bianchi-IX cosmological model it is shown that a normalizable wave function of the universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Schrödinger equation. The Wheeler–DeWitt quantum geometrodynamics is represented a singular, BRST-invariant solution to the Schrödinger equation having no property of normalizability.

scholarly journals TIME IN QUANTUM GEOMETRODYNAMICS

2000 ◽  
Vol 15 (26) ◽  
pp. 4125-4140
Author(s):  
ARKADY KHEYFETS ◽  
WARNER A. MILLER
Keyword(s):  
Standard Approach ◽  
General Covariance ◽  
Quantization Procedure ◽  
Total Problem ◽  
Quantum Geometrodynamics ◽  
Dynamic Variables

We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general covariance symmetries. The resulting theory, unlike the standard approach, takes into account the states that are off shell with respect to the constraints, and thus avoids the problems of time. In this approach, quantum geometrodynamics, general covariance, and the interpretation of time emerge together as parts of the solution of the total problem of geometrodynamic evolution.

The intrinsic helicity of elementary particles and the spin-statistic connection

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560004 ◽  
Author(s):  
Francesco De Martini ◽  
Enrico Santamato
Keyword(s):  
Complete Solution ◽  
Pauli Exclusion Principle ◽  
Elementary Particles ◽  
Exclusion Principle ◽  
Uncertainty Relations ◽  
Standard Quantum ◽  
Einstein Podolsky Rosen ◽  
Non Local ◽  
Spin Statistic ◽  
Quantum Geometrodynamics

The traditional standard quantum mechanics (SQM) is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli exclusion principle". The present paper presents a simple and complete solution of the spin-statistics problem on the basis of the "conformal quantum geometrodynamics (CQG)", a theory that was found to reproduce successfully all relevant processes of the SQM based on Dirac's or Schrödinger's equations, including Heisenberg's uncertainty relations and non-local Einstein–Podolsky–Rosen (EPR) correlations. When applied to a system made of many identical particles, an additional property of all elementary particles enters naturally into play: the "intrinsic helicity". This property, not considered in the SQM, determines the correct spin-statistics connection (SSC) observed in nature.

scholarly journals Quantum geometrodynamics with intrinsic time development

2016 ◽  
Vol 25 (13) ◽  
pp. 1645008 ◽  
Author(s):  
Chopin Soo
Keyword(s):  
Paradigm Shift ◽  
Time Development ◽  
Gauge Invariant ◽  
Problem Of Time ◽  
Diffeomorphism Invariance ◽  
Intrinsic Time ◽  
Natural Extensions ◽  
The Universe ◽  
Quantum Geometrodynamics ◽  
Einstein’S General Relativity

Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full spacetime covariance to spatial diffeomorphism invariance yields a nonvanishing Hamiltonian, a resolution of the ‘problem of time’ and gauge-invariant temporal ordering in an ever expanding universe. Einstein’s general relativity is a particular realization of a wider class of theories; and the framework prompts natural extensions and improvements with the consequent dominance of Cotton–York potential at early times when the universe was small.

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