scholarly journals Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Entropy ◽  
2018 ◽  
Vol 20 (3) ◽  
pp. 205 ◽  
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
Quantum Gravity ◽  
Gravity Theory ◽  
Covariant Quantum ◽  
Generalized Lagrangian

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 Los principios de la relatividad: una introducci´on pedag´ogica

2018 ◽  
Vol 64 (1) ◽  
pp. 87
Author(s):  
Y. Bonder ◽  
E. Okon
Keyword(s):  
Quantum Gravity ◽  
Gravity Theory ◽  
Theory Of Relativity

The principles underlying the theory of relativity, special and general, are presented. An easy to follow and pedagogical language is used and, based on physical examples, the motivation and some consequences of such principles are discussed. In addition, some roles of these principles when looking for a quantum gravity theory are mentioned

scholarly journals Collision Space-Time.  Unified Quantum Gravity. Gravity is Lorentz Symmetry Break Down at the Planck Scale

2019 ◽  
Author(s):  
Espen Haug
Keyword(s):  
Wave Equation ◽  
Quantum Gravity ◽  
Planck Scale ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Gravity Theory ◽  
Relativistic Wave Equation ◽  
Relativistic Energy ◽  
Modern Physics ◽  
Heisenberg Uncertainty

We have recently presented a unified quantum gravity theory [1]. Here we extend on that work and present an even simpler version of that theory. For about hundred years, modern physics has not been able to build a bridge between quantum mechanics and gravity. However, a solution may be found here; we present our quantum gravity theory, which is rooted in indivisible particles where matter and gravity are related to collisions and can be described by collision space-time. In this paper, we also show that we can formulate a quantum wave equation rooted in collision space-time, which is equivalent to mass and energy.The beauty of our theory is that most of the main equations that currently exist in physics are not changed (in terms of predictions), except at the Planck scale. The Planck scale is directly linked to gravity and gravity is, surprisingly, actually a Lorentz symmetry as well as a form of Heisenberg uncertainty break down at the Planck scale. Our theory gives a dramatic simplification of many physics formulas without altering the output predictions. The relativistic wave equation, the relativistic energy momentum relation, and Minkowski space can all be represented by simpler equations when we understand mass at a deeper level. This not attained at a cost, but rather a reflection of the benefit in having gravity and electromagnetism unified under the same theory.

NONRENORMALIZABILITY MAY BE SUPERFICIAL IN THE COVARIANT FORMALISM OF QUANTUM GRAVITY

1995 ◽  
Vol 10 (21) ◽  
pp. 1501-1506 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Perturbation Theory ◽  
Quantum Gravity ◽  
Ad Hoc ◽  
Einstein Gravity ◽  
Gravity Theory ◽  
Usual Sense ◽  
Covariant Formalism ◽  
Perturbative Approach

It is pointed out that the nonrenormalizability of quantum Einstein gravity may be caused by the inadequacy of the conventional perturbative approach. It is more reasonable to reconsider the problem in the light of a newly proposed perturbative scheme, which is free of the ad hoc assumption on which the conventional perturbation theory is based. It is explicitly shown that there is a gravity-theory example which is nonrenormalizable in the usual sense but completely finite if the new perturbative scheme is applied.

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.

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