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.
DERELİ, TEKİN; KOÇAK, ŞAHİN; and LİMONCU, MURAT (2006) "Degenerate Spin Structures and the Lévy-Leblond Equation," Turkish Journal of Physics: Vol. 30: No. 5, Article 6. Available at: https://journals.tubitak.gov.tr/physics/vol30/iss5/6