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Dirac Hamiltonian formulation and algebra of the constraints in the Einstein - Cartan theory

I A Nikolic

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We present here a detailed but rather transparent Dirac Hamiltonian formulation of the first-order Einstein - Cartan theory of gravitation, including a rigorous derivation of the off-shell constraint algebra between lapse, shift and Lorentz Hamiltonians. Taking the simplest solution for determined multipliers, it is shown that squares of the second-class constraints appear on the right-hand side of the Poisson brackets algebra.


PACS

04.60.-m Quantum gravity

04.50.-h Higher-dimensional gravity and other theories of gravity

MSC

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

17B63 Poisson algebras

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

Subjects

Gravitation and cosmology

Dates

Issue 12 (December 1995)

Received 13 March 1995, in final form 22 August 1995



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