Geodesics in Minkowski Setup
September 22, 2025
 
The classical construction of the symplectic struc-ture on the space of geodesic trajectories via Hami-ltonian reduction fails in the pseudo-Riemannian setting due to a dimensional mismatch created by the null geodesics. This paper proposes a new, unified approach. We first construct the space of all geodesic trajectories directly as the quotient of the space of geodesics curves by the affine reparame-trization group. Then, we in troduce a canonical Submitted for publication.
object, the “conformal co-symplectic” structure, defined by pushing forward the conformal class of the inverse of the original symplectic form. In particular, on the null geodesics, the image of this structure is a codimension-1 distribution that we prove is the canonical contact structure. NOTE: This paper is the formalization of the content of the letter to Sergei Tabachnikov on the subject I sent in May 2006A4DF9FB4-E2B8-4F1E-A18A-85B473E73E43.htmlshapeimage_4_link_0