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@article{59482, author = {Tessarotto, Massimo and Cremaschini, Claudio}, article_number = {2}, doi = {http://dx.doi.org/10.3390/e23020215}, keywords = {Einstein-Hilbert variational principle;Hamiltonian theory of GR;ADM Hamiltonian theory;manifest covariance}, language = {eng}, issn = {1099-4300}, journal = {Entropy}, title = {The Principle of Covariance and the Hamiltonian Formulation of General Relativity}, url = {https://www.mdpi.com/1099-4300/23/2/215}, volume = {23}, year = {2021} }
TY - JOUR ID - 59482 AU - Tessarotto, Massimo - Cremaschini, Claudio PY - 2021 TI - The Principle of Covariance and the Hamiltonian Formulation of General Relativity JF - Entropy VL - 23 IS - 2 SP - "215-1"-"215-33" EP - "215-1"-"215-33" SN - 10994300 KW - Einstein-Hilbert variational principle;Hamiltonian theory of GR;ADM Hamiltonian theory;manifest covariance UR - https://www.mdpi.com/1099-4300/23/2/215 N2 - The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out. ER -
TESSAROTTO, Massimo a Claudio CREMASCHINI. The Principle of Covariance and the Hamiltonian Formulation of General Relativity. \textit{Entropy}. 2021, roč.~23, č.~2, s.~''215-1''-''215-33'', 33 s. ISSN~1099-4300. Dostupné z: https://dx.doi.org/10.3390/e23020215.
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