Bargmann structures and Newton-Cartan theory

作者：Christian Duval, Guy Burdet, H. P. Künzle, M. Perrin · 发表于：Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 年份：1985 · DOI：10.1103/physrevd.31.1841 · 被引用次数：420 · 研究领域：Relativity and Gravitational Theory、Algebraic and Geometric Analysis、Noncommutative and Quantum Gravity Theories

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 Schr\"odinger equation into a purely covariant form. The Newton-Cartan field equations are readily derived from Einstein's Lagrangian on the space-time extension.