scholarly journals The volume operator in covariant quantum gravity

2010 ◽  
Vol 27 (16) ◽  
pp. 165003 ◽  
Author(s):  
You Ding ◽  
Carlo Rovelli
Keyword(s):  
Quantum Gravity ◽  
Covariant Quantum ◽  
Volume Operator

scholarly journals Hamilton–Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 592 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Quantum Gravity ◽  
Evolution Equations ◽  
Wave Theory ◽  
Gravity Theory ◽  
Principal Function ◽  
Canonical Momentum ◽  
Covariant Quantum ◽  
Canonical Variables ◽  
Canonical State ◽  
Scalar Type

The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder–Weyl variational formulation (2015–2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable g μ ν being realized by the third-order 4-tensor Π μ ν α . It is shown that this generates a corresponding Hamilton–Jacobi theory in which the Hamilton principal function is a 4-tensor S α . However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton–Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field.

scholarly journals Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 418 ◽  
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
Quantum Gravity ◽  
Gaussian Function ◽  
Quantum Probability ◽  
De Sitter ◽  
Covariant Quantum ◽  
Generalized Lagrangian ◽  
Quantum Wave ◽  
H Theorem

Based on the introduction of a suitable quantum functional, identified here with the Boltzmann–Shannon entropy, entropic properties of the quantum gravitational field are investigated in the framework of manifestly-covariant quantum gravity theory. In particular, focus is given to gravitational quantum states in a background de Sitter space-time, with the addition of possible quantum non-unitarity effects modeled in terms of an effective quantum graviton sink localized near the de Sitter event horizon. The theory of manifestly-covariant quantum gravity developed accordingly is shown to retain its emergent-gravity features, which are recovered when the generalized-Lagrangian-path formalism is adopted, yielding a stochastic trajectory-based representation of the quantum wave equation. This permits the analytic determination of the quantum probability density function associated with the quantum gravity state, represented in terms of a generally dynamically-evolving shifted Gaussian function. As an application, the study of the entropic properties of quantum gravity is developed and the conditions for the existence of a local H-theorem or, alternatively, of a constant H-theorem are established.

scholarly journals The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1209
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
Quantum Gravity ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Mathematical Formulation ◽  
Relativistic Quantum Mechanics ◽  
Covariant Quantum ◽  
Conjugate Momentum ◽  
Starting Point ◽  
The Subject ◽  
Suitable Notion

The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated.

scholarly journals Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 511
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Event Horizon ◽  
Field Equations ◽  
Central Mass ◽  
Event Horizons ◽  
Covariant Quantum ◽  
Gravitational Fields ◽  
New Type

A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width δr between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as δr∼M3; (b) for supermassive black holes δr is typically orders of magnitude larger than the Planck length lP. Instead, for typical stellar-mass black holes, δr may drop well below lP. The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons.

Ground state of the universe in quantum cosmology

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641014 ◽  
Author(s):  
Natalia Gorobey ◽  
Alexander Lukyanenko
Keyword(s):  
Quantum Gravity ◽  
Ground State ◽  
Quantum Dynamics ◽  
Homogeneous Model ◽  
Cosmic Time ◽  
Matter Content ◽  
Closed Universe ◽  
Initial State ◽  
Covariant Quantum ◽  
The Universe

We find a physical state of a closed universe with the minimal excitation of the universe expansion energy in quantum gravity. It is an analog of the vacuum state of the ordinary quantum field theory in the Minkowsky space, but in our approach an energy of space of a closed universe together with the energy of its matter content are minimized. This ground state is chosen among an enlarged set of physical states, compared with the ordinary covariant quantum gravity. In our approach, physical states are determined by weak constraints: quantum mechanical averages of gravitational constraint operators equal zero. As a result, they appear to be non-static in such a modification of quantum gravity. Quantum dynamics of the universe is described by Schrödinger equation with a cosmic time determined by weak gravitational constraints. In order to obtain the observed megascopic universe with the inflation stage just after its quantum beginning, a lot of the energy in the form of the inflaton scalar field condensate is prescribed to the initial state. Parameters of the initial state for a homogeneous model of the universe are calculated.

One-loop diagrams in quantum gravity coupled to scalar electrodynamics

2019 ◽  
Vol 28 (08) ◽  
pp. 1950100
Author(s):  
Hyun Ju Go
Keyword(s):  
Quantum Gravity ◽  
Heat Kernel ◽  
Equation Of Motion ◽  
The Other ◽  
Covariant Quantum ◽  
Heat Kernel Expansion ◽  
Fermionic Loop ◽  
Low Probability ◽  
Single Field ◽  
Existing Result

In nonsupersymmetric-covariant quantum gravity theory, for each system of gravity coupled with single field is one-loop divergent. There were two kinds of methods to reach this result: diagrammatic calculation and heat kernel expansion. On the other hand, more symmetry requirements make the theory finite and it was analyzed how it is possible. In this paper, based on diagrammatic calculation, we consider Einstein–Scalar electrodynamics (Einstein–SQED) system which is the simplest model among the systems of gravity coupled with multiple fields having their own interaction. Although it is known that fermionic loop can cancel the divergent terms as in the case of supersymmetric theory, there might be accidental cancellation by the equation of motion at a low probability. It is worth to study because there is no such attempt for this model yet and it can be checked easily using the existing result. We introduce how to calculate the possible one-loop diagrams in Einstein–SQED system and show how divergent terms are not vanished with the results calculated earlier.

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