The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity
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.
scientific article; zbMATH DE number 3907314
scientific article