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THE STOCHASTIC QUANTIZATION OF THE GRAVITATIONAL-FIELD AND THE GRIBOV PROBLEM

open access: yesTHE STOCHASTIC QUANTIZATION OF THE GRAVITATIONAL-FIELD AND THE GRIBOV PROBLEM
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On the Quantization of Einstein's Gravitational Field Equations

Physical Review, 1950
Weiss' method of quantization of field theories characterized by first-order Lagrangians can be carried out in a non-metrical "amorphous" space, as was first stated by Bergmann and Brunings. The gravitational equations can be regarded as differential equations for the field variables ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ in an amorphous space and ...
A Schild
exaly   +2 more sources

Covariant quantization of the gravitational field

Il Nuovo Cimento, 1961
In any quantum theory, in which the metric tensor of Einstein’s gravitational theory is also quantized, it becomes meaningless to ask for an initial space-like surface on which to specify the conventional field commutators. The covariant quantum formalism, in which all fields either commute or fail to do so only when the field’s points coincide, is ...
J. Klauder
semanticscholar   +5 more sources

Asymptotic Quantization of the Gravitational Field

Physical Review Letters, 1981
A new approach to quantum gravity is proposed. The framework is sufficiently general to handle nontrivial space-time topologies required, e.g., in the black-hole formation and evaporation processes, and yet it incorporates notions such as energy-momentum, angular momentum, spin, mass, and discrete symmetries, normally associated with the Poincar\'e ...
A. Ashtekar
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Canonical Quantization of Gravitational Field

Physical Review, 1968
The six dynamical variables gmn(x) are expressed in terms of three "coordinatelike" variables yA(x) and three invariant variables γα(k). The longitudinal constraints Rn0+Tn0=0 imply the vanishing of the momenta canonically conjugate to the yA(x), and the only remaining constraint can be written invariantly in terms of the γα(k), their conjugate momenta,
A. Peres
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Gravitational Field: Equivalence of Feynman Quantization and Canonical Quantization

Physical Review, 1964
The transition amplitude for the gravitational field as given by the Feynman sum over histories expression is analyzed in analogy to the electromagnetic transition amplitude. The analysis is based on an explicit representation of the Feynman sum by means of a lattice.
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Quantization of Einstein's Gravitational Field: General Treatment

Proceedings of the Physical Society Section A, 1952
The quantization of the complete gravitational field is carried out by extending the work of an earlier paper. The main obstacles in the quantization of Einstein's field are overcome by expressing the field quantities in the Riemannian space as expansions in the flat space, and then splitting the gravitational field into the linear and the non-linear ...
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Quantization of Einstein's Gravitational Field Equations. II

Physical Review, 1952
Explicit expressions are obtained for all the constraints which appear in the canonical formulation of the field equations of general relativity and of electrodynamics.
A Schild
exaly   +3 more sources

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