The Principle of Covariance and the Hamiltonian Formulation of General Relativity

@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.