Gravitational Field: Equivalence of Feynman Quantization and Canonical Quantization

1964 ◽  
Vol 134 (5B) ◽  
pp. B1155-B1182 ◽  
Author(s):  
H. Leutwyler
Keyword(s):  
Gravitational Field ◽  
Canonical Quantization ◽  
Feynman Quantization

scholarly journals Foundations of a Theory of Gravity with a Constraint and Its Canonical Quantization

2021 ◽  
Vol 52 (1) ◽  
Author(s):  
Alexander P. Sobolev
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Early Universe ◽  
Canonical Quantization ◽  
Entropy Density ◽  
Maximum Temperature ◽  
Past Century ◽  
Physical Point ◽  
Theory Of Gravity ◽  
The Universe

AbstractThe gravitational equations were derived in general relativity (GR) using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such equality of all coordinate systems may not correspond to reality. Nevertheless, no actual verification of the necessity of this assumption has been made to date. The paper proposes a theory of gravity with a constraint, the degenerate variants of which are general relativity (GR) and the unimodular theory of gravity. This constraint is interpreted from a physical point of view as a sufficient condition for the adiabaticity of the process of the evolution of the space–time metric. The original equations of the theory of gravity with the constraint are formulated. On this basis, a unified model of the evolution of the modern, early, and very early Universe is constructed that is consistent with the observational astronomical data but does not require the hypotheses of the existence of dark energy, dark matter or inflatons. It is claimed that: physical time is anisotropic, the gravitational field is the main source of energy of the Universe, the maximum global energy density in the Universe was 64 orders of magnitude smaller the Planckian one, and the entropy density is 18 orders of magnitude higher the value predicted by GR. The value of the relative density of neutrinos at the present time and the maximum temperature of matter in the early Universe are calculated. The wave equation of the gravitational field is formulated, its solution is found, and the nonstationary wave function of the very early Universe is constructed. It is shown that the birth of the Universe was random.

scholarly journals Black Holes, Gravitational Waves and Quantum Gravity

2021 ◽  
pp. 1-11
Author(s):  
W. F. Chagas-Filho
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Gravitational Waves ◽  
Loop Quantum Gravity ◽  
Canonical Quantization ◽  
Planck Length ◽  
Basic Ideas ◽  
Area And Volume

Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric quantities such as area and volume are quantized in terms of the Planck length. In this paper we present the basic ideas for a future, mathematically more rigorous, attempt to combine black holes and gravitational waves using the quantization of geometric quantities introduced by Loop Quantum Gravity.

scholarly journals Energy Spectrum for Gravitational Waves

2020 ◽  
pp. 24-31
Author(s):  
W. F. Chagas- Filho
Keyword(s):  
General Relativity ◽  
Wave Propagation ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Loop Quantum Gravity ◽  
Canonical Quantization ◽  
Minimum Length ◽  
Speed Of Light ◽  
Basic Equations ◽  
Area And Volume

Loop Quantum Gravity (LQG) is a formalism for describing the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity (GR). The most important result of LQG is that geometric quantities such as area and volume are not arbitrary but are quantized in terms of a minimum length. In this paper we investigate the possibility of combining the notion of a minimum length with the basic equations that describe wave propagation. We find that the minimum length, combined with the constancy of the speed of light, induces a natural spectrum for the energy of a gravitational wave.

Canonical Quantization of Gravitational Field

1968 ◽  
Vol 171 (5) ◽  
pp. 1335-1344 ◽  
Author(s):  
Asher Peres
Keyword(s):  
Gravitational Field ◽  
Canonical Quantization

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.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Evolution of collisional systems

1984 ◽  
Vol 75 ◽  
pp. 361-362
Author(s):  
André Brahic
Keyword(s):  
Gravitational Field ◽  
Dynamical Evolution ◽  
Oblate Planet

AbstractThe dynamical evolution of planetary discs in the gravitational field of an oblate planet and a satellite is numerically simulated.

Sedimentation of charged colloids in the gravitational field : Relaxation toward equilibrium

2000 ◽  
Vol 10 (PR5) ◽  
pp. Pr5-109-Pr5-112
Author(s):  
J.-F. Dufrêche ◽  
J.-P. Simonin ◽  
P. Turq
Keyword(s):  
Gravitational Field ◽  
Charged Colloids

Pair Production in a Field of Heavy Nuclei and in a Gravitational Field

1971 ◽  
Vol 105 (12) ◽  
pp. 780-781 ◽  
Author(s):  
Ya.B. Zel'dovich ◽  
Lev P. Pitaevskii ◽  
Valentin S. Popov ◽  
Aleksei A. Starobinskii
Keyword(s):  
Gravitational Field ◽  
Pair Production ◽  
Heavy Nuclei
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