Covariant canonical formalism for gravity |
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| Affiliation: | 1. Theoretical Physics Department, CERN, Geneva, Switzerland;2. Institute for Particle Physics Phenomenology, Department of Physics, Durham University, Durham DH1 3LE, UK;3. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK;1. Weizmann Institute of Science, Rehovot, Israel;2. School of Mathematics, University of Edinburgh, Edinburgh, UK;1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China;2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China;1. CEICO, Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 21 Prague 8, Czech Republic;2. Institute for Theoretical Physics, Spinoza Institute & EMMEΦ, Utrecht University, Buys Ballot Building, Princetonplein 5, 3584 CC Utrecht, the Netherlands |
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| Abstract: | ![]()
We continue the previous discussion (A. D'Adda, J. E. Nelson, and T. Regge, Ann. Phys. (N.Y.)165) of the covariant canonical formalism for the group manifold and relate it to the standard canonical vierbein formalism as pioneered by Dirac. The form bracket is related to the Poisson bracket of classical mechanics. We utilise systematically the calculus of differential forms and a compound notation which labels Poincaré multiplets. In this way we obtain a particularly clear and compact expression for the Hamiltonian and the constraints algebra of the vierbein formalism. |
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