Geometric structures of the classical general relativistic phase space

JANYŠKA, Josef and Marco MODUGNO. Geometric structures of the classical general relativistic phase space. International Journal of Geometrical Methods in Modern Physics. World Scientific, 2008, vol. 5, No 5, p. 699-754. ISSN 0219-8878.

Basic information

Original name

Geometric structures of the classical general relativistic phase space

Name in Czech

Geometrické struktury klasického obecně relativistického fázového prostoru

Authors

JANYŠKA, Josef (203 Czech Republic, guarantor) and Marco MODUGNO (380 Italy)

Edition

International Journal of Geometrical Methods in Modern Physics, World Scientific, 2008, 0219-8878

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Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.464

RIV identification code

RIV/00216224:14310/08:00024916

Organization unit

Faculty of Science

UT WoS

000259928300004

Keywords in English

Spacetime; phase space; spacetime connection; phase connection; Schouten bracket; Froelicher Nijenhuis bracket; symplectic structure; Poisson structure; Jacobi structure

Tags

Froelicher Nijenhuis bracket, Jacobi structure, phase connection, phase space, Poisson structure, Schouten bracket, spacetime, spacetime connection, symplectic structure

Tags

International impact, Reviewed

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Abstract

V originále

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialise these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well.

In Czech

Článek se zabývá geometrickými vlastnostmi fázového prostoru klasické obecně-relativistické částice. Fázový prostor je chápán jako prostor 1-jetů pohybů. Hlavním cílem je určit geometrické struktury, které jsou dány Lorentzovou metrikou a fázovou konexí. Dostáváme tak podmínky pro kontaktní a Jakobiho strukturu.

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Links

GA201/05/0523, research and development project	Name: Geometrické struktury na fibrovaných varietách Investor: Czech Science Foundation, Geometric structures on fibered manifolds
MSM0021622409, plan (intention)	Name: Matematické struktury a jejich fyzikální aplikace Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications