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 cosymplectic 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. Keywords: Spacetime, phase space, spacetime connection, phase connection, Schouten bracket, Froelicher-Nijenhuis bracket, symplectic structure, Poisson structure, Jacobi structure. MSC 2001: 53B15, 53B30, 53B50, 53D05, 53D17, 58A10, 58A20, 58A32.

Geometric structures of the classical general relativistic phase space / M.Modugno; J.Janyska. - In: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. - ISSN 0219-8878. - STAMPA. - 5, N. 5:(2008), pp. 1-56. [10.1142/S021988780800303X]

Geometric structures of the classical general relativistic phase space

MODUGNO, MARCO;
2008

Abstract

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 cosymplectic 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. Keywords: Spacetime, phase space, spacetime connection, phase connection, Schouten bracket, Froelicher-Nijenhuis bracket, symplectic structure, Poisson structure, Jacobi structure. MSC 2001: 53B15, 53B30, 53B50, 53D05, 53D17, 58A10, 58A20, 58A32.
2008
5, N. 5
1
56
M.Modugno; J.Janyska
File in questo prodotto:
File Dimensione Formato  
3 Phase space.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 621.29 kB
Formato Adobe PDF
621.29 kB Adobe PDF   Richiedi una copia
3-Phase-Space.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 43.36 kB
Formato Adobe PDF
43.36 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/344442
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 11
social impact