Degenerate Spin Structures and the Levy-Leblond Equation

Abstract

Newton-Cartan manifolds and the Galilei group are defined by the use of co-rank one degenerate metric tensor. Newton-Cartan connection is lifted to the degenerate spinor bundle over a Newton-Cartan 4-manifold by the aid of degenerate spin group. Levy-Leblond equation is constructed with the lifted connection.

Paper presented at The 5th Workshop on Quantization, Dualities and Integrable Systems, Pamukkale University, 23-28 January 2006, Denizli, Turkey