The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity
type: Item
instance of: scholarly article
title: The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity
zbMATH Open document ID: 0568.53036
DOI: 10.1016/0003-4916(84)90122-2
author: Wiktor Szczyrba
published in: Annals of Physics
publication date: 1984-01-01T00:00:00Z
review text: The Einstein-Cartan-Sciama-Kibble theory (ECSK) is a gauge theory of gravity having SO(3,1) covariance and gravitational Lagrangian coinciding with that of General Relativity; the different matter fields are described by tensor fields subject to the variational equations of suitable Lagrangians. In the present paper a Hamiltonian formulation of the ECSK theory is developed and analyzed in detail, mainly from the point of view of constraints and evolution equations. It is found that the theory can be reduced to seven gravitational constraints, and eighteen gravitational dynamical equations; while twelve of the field equations are solved, eliminating twelve variables. An initial value formulation of the ECSK theory is also presented and analyzed in the spirit of Arnowitt, Deser, and Misner. The paper also offers detailed introductions, supplemented by extensive bibliography, to subjects as variational principles, choices of Lagrangians for different matter fields, treatment of constraints, compatibility of constraints with evolution equations, symplectic structures, initial value formalisms, and conservation laws.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83D05
zbMATH DE Number: 3907314
zbMATH Keywords: Hamiltonian formalism
zbMATH Keywords: Einstein-Cartan-Sciama-Kibble theory
zbMATH Keywords: gauge theory
zbMATH Keywords: gravity
zbMATH Keywords: variational principles
zbMATH Keywords: evolution equations
zbMATH Keywords: symplectic structures
zbMATH Keywords: conservation laws
MaRDI profile type: Publication
full work available at URL: 0003-4916(84)90122-2
OpenAlex ID: W2048549889
cites work: Q3246860
cites work: Lorentz Invariance and the Gravitational Field
cites work: Q5849608
cites work: Q5724559
cites work: Energy of the Gravitational Field
cites work: Consistency of the Canonical Reduction of General Relativity
cites work: Q5328018
cites work: The Large Scale Structure of Space-Time
cites work: Q3889735
cites work: Gravitational field as a generalized gauge field.
cites work: Q5182273
cites work: Q3940446
cites work: Q3854284
cites work: Q4173918
cites work: Gravity as an internal Yang-Mills gauge field theory of the Poincaré group
cites work: Q3322013
cites work: On the Analogy Between Classical and Quantum Mechanics
cites work: Dirac Bracket Transformations in Phase Space
cites work: Presymplectic manifolds and the Dirac–Bergmann theory of constraints
cites work: Constrained dynamics. With applications to Yang-Mills theory, general relativity, classical spin, dual string model
cites work: Q4167627
cites work: Q5822608
cites work: Differential geometry and the calculus of variations
cites work: Q5682259
cites work: The Hamilton-Cartan formalism in the calculus of variations
cites work: Lagrangian formalism in the classical field theory
cites work: A canonical structure for classical field theories
cites work: Symplectic approach to the theory of quantized fields. II
cites work: Geometric quantization and multiplicities of group representations
cites work: Q3849781
cites work: A Hamiltonian structure of the interacting gravitational and matter fields
cites work: Geometrization of the classical field theory and its application in Yang- Mills field theory
cites work: Q4376389
cites work: A symplectic framework for field theories
cites work: The Einstein Equations of Evolution-A Geometric Approach
cites work: Q4074046
cites work: The structure of the space of solutions of Einstein's equations. II: Several Killing fields and the Einstein-Yang-Mills equations
cites work: Spin and torsion in general relativity. I: Foundations. II: Geometry and field equations
cites work: General relativity with spin and torsion: Foundations and prospects
cites work: Integral Formalism for Gauge Fields
cites work: Canonical Variables for the Interacting Gravitational and Dirac Fields
cites work: Gravitational fields, spinor fields, and groups of motions
cites work: The Einstein-Cartan theory of gravitation in a Hamiltonian form.
cites work: Variational formulation of general relativity from 1915 to 1925 ''Palatini's method'' discovered by Einstein in 1925
cites work: Spinor Structure of Space-Times in General Relativity. II
cites work: Q5731354
cites work: The canonical variables, the symplectic structure and the initial value formulation of the generalized Einstein-Cartan theory of gravity
cites work: On the equivalence of the relativistic theories of gravitation
cites work: Existence of differentiable structure in the set of submanifolds. An attempt of geometrization of calculus of variations
cites work: Q4136234
cites work: Q5337746
cites work: A Hamiltonian formulation of the Einstein-Cartan-Sciama-Kibble theory of gravity
cites work: The neutrino problem in cosmology
Recommended article: The phase structure of Einstein-Cartan theory
Recommended article: The general relativity dynamics in the Eisenhart geometry
Recommended article: Kinematics and dynamics of \(f(R)\) theories of gravity
Recommended article: Dynamical \(F(R)\) gravities

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity (Recommended article)
Recommended article: Structure of the spacetime under gravitation obtained by purely dynamical method
Similarity Score: 0.8877067
Recommender Run: Recommender Run 3

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity (Recommended article)
Recommended article: Erratum to: ``Einstein-Cartan gravity, matter, and scale-invariant generalization''
Similarity Score: 0.8873581
Recommender Run: Recommender Run 3

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity (Recommended article)
Recommended article: GRAVITATIONAL THEORY WITH A DYNAMICAL SPACE–TIME
Similarity Score: 0.88549113
Recommender Run: Recommender Run 3

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity (Recommended article)
Recommended article: The dynamics of metric-affine gravity
Similarity Score: 0.8846944
Recommender Run: Recommender Run 3

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity (Recommended article)
Recommended article: The dynamics of strong coupling gravity
Similarity Score: 0.88443726
Recommender Run: Recommender Run 3

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity (Recommended article)
Recommended article: The dynamical viability of scalar–tensor gravity theories
Similarity Score: 0.8844001
Recommender Run: Recommender Run 3