CREMASCHINI, Claudio and Massimo TESSAROTTO. Hamilton-Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity. Symmetry. 2019, vol. 11, No 4, p. "592-1"-"592-26", 26 pp. ISSN 2073-8994. Available from: https://dx.doi.org/10.3390/sym11040592.
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Basic information
Original name Hamilton-Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity
Authors CREMASCHINI, Claudio (380 Italy, guarantor, belonging to the institution) and Massimo TESSAROTTO (380 Italy, belonging to the institution).
Edition Symmetry, 2019, 2073-8994.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10308 Astronomy
Country of publisher Switzerland
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19240/19:A0000554
Organization unit Faculty of Philosophy and Science in Opava
Doi http://dx.doi.org/10.3390/sym11040592
UT WoS 000467314400151
Keywords in English covariant quantum gravity; Hamilton equations; Hamilton-Jacobi theory; wave theory; massive; massless gravitons
Tags FÚ, RCTPA, RIVOK
Tags International impact, Reviewed
Changed by Changed by: RNDr. Jan Hladík, Ph.D., učo 25379. Changed: 22/3/2020 07:11.
Abstract
The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder-Weyl variational formulation (2015-2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable g_(mu nu) being realized by the third-order 4-tensor Pi_(mu nu)^alpha. It is shown that this generates a corresponding Hamilton-Jacobi theory in which the Hamilton principal function is a 4-tensor S^alpha . However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton-Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field.
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