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 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.

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.

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 SPIN-CUBE MODELS OF QUANTUM GRAVITY

2013 ◽  
Vol 25 (10) ◽  
pp. 1343008 ◽  
Author(s):  
A. MIKOVIĆ
Keyword(s):  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Path Integral ◽  
Classical Limit ◽  
Edge Length ◽  
The State ◽  
Regge Model ◽  
Bf Theory ◽  
Spin Foam Models ◽  
Spin Foam

We study the state-sum models of quantum gravity based on a representation 2-category of the Poincaré 2-group. We call them spin-cube models, since they are categorical generalizations of spin-foam models. A spin-cube state sum can be considered as a path integral for a constrained 2-BF theory, and depending on how the constraints are imposed, a spin-cube state sum can be reduced to a path integral for the area-Regge model with the edge-length constraints, or to a path integral for the Regge model. We also show that the effective actions for these spin-cube models have the correct classical limit.

scholarly journals SYNCHRONOUS QUANTUM GRAVITY

2008 ◽  
Vol 23 (08) ◽  
pp. 1149-1156
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Reference Frame ◽  
Quantum Level ◽  
Covariance Principle

The implications of restricting the covariance principle within a Gaussian gauge are developed both on a classical and a quantum level. Hence, we investigate the cosmological issues of the obtained Schrödinger Quantum Gravity with respect to the asymptotically early dynamics of a generic Universe. A dualism between time and the reference frame fixing is then inferred.

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.

Small matrix modular path integral: iterative quantum dynamics in space and time

2021 ◽  
Author(s):  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Quantum Dynamics ◽  
Matrix Decomposition ◽  
Propagation Time ◽  
Molecular Aggregates ◽  
Space And Time ◽  
Small Matrix

This work presents a small matrix decomposition of the modular path integral for spin arrays or molecular aggregates, which leads to an iterative treatment with respect to the units that comprise the system and the propagation time.

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.

Sign in / Sign up

Export Citation Format

Share Document