Bargmann structures and Newton-Cartan theory

Journal Article · Mon Apr 15 04:00:00 EST 1985 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.31.1841· OSTI ID:5816991

Duval, C; Burdet, G; Kuenzle, H P; Perrin, M

It is shown that Newton-Cartan theory of gravitation can best be formulated on a five-dimensional extended space-time carrying a Lorentz metric together with a null parallel vector field. The corresponding geometry associated with the Bargmann group (nontrivially extended Galilei group) viewed as a subgroup of the affine de Sitter group AO(4,1) is thoroughly investigated. This new global formalism allows one to recast classical particle dynamics and the Schroedinger equation into a purely covariant form. The Newton-Cartan field equations are readily derived from Einstein's Lagrangian on the space-time extension.

• Research Organization: Centre de Physique Theorique, Centre National de la Recherche Scientifique, Luminy Case 907, 13288 Marseille, France
• OSTI ID: 5816991
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 31:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATION
INVARIANCE PRINCIPLES
KALUZA-KLEIN THEORY
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SPACE-TIME
UNIFIED-FIELD THEORIES
VECTOR FIELDS
WAVE EQUATIONS