Hamilton-Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19240%2F19%3AA0000554" target="_blank" >RIV/47813059:19240/19:A0000554 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2073-8994/11/4/592" target="_blank" >https://www.mdpi.com/2073-8994/11/4/592</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym11040592" target="_blank" >10.3390/sym11040592</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Hamilton-Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Hamilton-Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Symmetry

ISSN

2073-8994

e-ISSN

—

Svazek periodika

11

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

26

Strana od-do

„592-1“-„592-26“

Kód UT WoS článku

000467314400151

EID výsledku v databázi Scopus

2-s2.0-85065465461