scholarly journals MINISUPERSPACE MODEL FOR REVISED CANONICAL QUANTUM GRAVITY

2004 ◽  
Vol 13 (08) ◽  
pp. 1703-1718 ◽  
Author(s):  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Reference Frame ◽  
Quantum Dynamics ◽  
Cosmological Solution ◽  
Canonical Quantization ◽  
Hamiltonian Operator ◽  
Big Bang ◽  
Dust Fluid ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

We present a reformulation of the canonical quantization of gravity, as referred to the minisuperspace; the new approach is based on fixing a Gaussian (or synchronous) reference frame and then quantizing the system via the reconstruction of a suitable constraint; then the quantum dynamics is re-stated in a generic coordinates system and it becomes dependent on the lapse function. The analysis follows a parallelism with the case of the non-relativistic particle and leads to the minisuperspace implementation of the so-called kinematical action as proposed in Ref. 1 (here almost coinciding also with the approach presented in Ref. 2). The new constraint leads to a Schrödinger equation for the system, i.e. to non-vanishing eigenvalues for the super-Hamiltonian operator; the physical interpretation of this feature relies on the appearance of a "dust fluid" (non-positive definite) energy density, i.e. a kind of "materialization" of the reference frame. As an example of minisuperspace model, we consider a Bianchi type IX Universe, for which some dynamical implications of the revised canonical quantum gravity are discussed. We also show how, on the classical limit, the presence of the dust fluid can have relevant cosmological issues. Finally we upgrade our analysis by its extension to the generic cosmological solution, which is performed in the so-called long-wavelength approximation. In fact, near the Big-Bang, we can neglect the spatial gradients of the dynamical variables and proceed to implement, in each space point, the same minisuperspace paradigm valid for the Bianchi IX model.

scholarly journals DUALISM BETWEEN PHYSICAL FRAMES AND TIME IN QUANTUM GRAVITY

2004 ◽  
Vol 19 (20) ◽  
pp. 1519-1527 ◽  
Author(s):  
SIMONE MERCURI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Reference Frame ◽  
Path Integral ◽  
Classical Limit ◽  
Quantum Dynamics ◽  
Einstein Equations ◽  
Quantum Level ◽  
Dust Fluid ◽  
Lapse Function ◽  
Canonical Quantum

In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as a first step, we develop the canonical quantum dynamics, starting from the Einstein equations in presence of a dust fluid and arrive at a Schrödinger evolution. Then, by fixing the lapse function in the path-integral of gravity, we get a Schrödinger quantum dynamics, of which eigenvalues problem provides the appearance of a dust fluid in the classical limit. The main issue of our analysis is to claim that a theory, in which the time displacement invariance, on a quantum level, is broken, is indistinguishable from a theory for which this symmetry holds, but a real reference fluid is included.

scholarly journals COSMOLOGICAL ISSUES FOR REVISED CANONICAL QUANTUM GRAVITY

2003 ◽  
Vol 12 (08) ◽  
pp. 1445-1458 ◽  
Author(s):  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Canonical Quantization ◽  
Cosmological Problem ◽  
Self Consistent ◽  
Dust Fluid ◽  
Canonical Quantum Gravity ◽  
External Time ◽  
Matter Component ◽  
Canonical Quantum

In a recent work1 we presented a reformulation of the canonical quantum gravity, based on adding the so-called kinematical term to the gravity-matter action. This revised approach leads to a self-consistent canonical quantization of the 3-geometries, which referred to the external time as provided via the added term. Here, we show how the kinematical term can be interpreted in terms of a non-relativistic dust fluid which plies the role of a "real clock" for the quantum gravity theory, and, in the WKB limit of a cosmological problem, makes account for a dark matter component which, at present time, could play a dynamical role.

scholarly journals Canonical Quantum Gravity, Constructive QFT, and Renormalisation

2020 ◽  
Vol 8 ◽  
Author(s):  
Thomas Thiemann
Keyword(s):  
Quantum Gravity ◽  
Quantum Dynamics ◽  
Statistical Physics ◽  
Gravitational Interaction ◽  
Quantum Field ◽  
Constructive Quantum Field Theory ◽  
Canonical Approach ◽  
Quantum Statistical ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the gravitational interaction, the corresponding Wheeler–DeWitt operator-valued distribution suffers from quantisation ambiguities that need to be fixed. In a very recent series of works, we have employed methods from the constructive quantum field theory in order to address those ambiguities. Constructive QFT trades quantum fields for random variables and measures, thereby phrasing the theory in the language of quantum statistical physics. The connection to the canonical formulation is made via Osterwalder–Schrader reconstruction. It is well known in quantum statistics that the corresponding ambiguities in measures can be fixed using renormalisation. The associated renormalisation flow can thus be used to define a canonical renormalisation programme. The purpose of this article was to review and further develop these ideas and to put them into context with closely related earlier and parallel programmes.

scholarly journals General Canonical Quantum Gravity Theory and that of the Universe and General Black Hole

2021 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang ◽  
Xinfei Li
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Nonlinear System ◽  
Quantum Gravity ◽  
Canonical Quantization ◽  
Gravity Theory ◽  
Canonical Momentum ◽  
Canonical Quantum Gravity ◽  
The Universe ◽  
Canonical Quantum

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

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.

ARITHMETIC QUANTUM GRAVITY

2010 ◽  
Vol 19 (14) ◽  
pp. 2305-2310 ◽  
Author(s):  
AXEL KLEINSCHMIDT ◽  
HERMANN NICOLAI
Keyword(s):  
Quantum Gravity ◽  
Algebraic Structure ◽  
Complete Resolution ◽  
Quantum Level ◽  
Cosmological Singularity ◽  
Quantum Billiard ◽  
Symmetry Structure ◽  
Canonical Quantum Gravity ◽  
The Universe ◽  
Canonical Quantum

The arithmetic chaos of classical (super)gravity near a spacelike singularity is elevated to the quantum level via the construction of a cosmological quantum billiard system. Its precise formulation, together with its underlying algebraic structure, allows for a general analysis of the wavefunction of the universe near the singularity. We argue that the extension of these results beyond the billiard approximation may provide a concrete mechanism for emergent space as well as new perspectives on several long-standing issues in canonical quantum gravity. The exponentially growing complexity of the underlying symmetry structure could introduce an element of non-computability that effectively "screens" the cosmological singularity from a complete resolution.

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