26 Jan 2026. Talk by Filip Moučka at the 34th Student conference: Winter School on Mathematical Physics in Jánské Lázně, Czech Republic.
Abstract: Replacing the minus sign in the canonical Poisson bracket by the plus sign yields a commutative bracket that nevertheless allows one to formulate Newton’s equations for conservative systems in close analogy with the standard Hamiltonian approach. Passing to the global setting, where the phase space is identified with the total space of the cotangent bundle, requires the introduction of an affine connection on the base manifold. The resulting geometric structure underlying the bracket on functions is no longer the canonical symplectic form, but rather the Patterson-Walker metric. I will give a brief overview of the induced phase space dynamics and outline an application to the study of singular geodesically invariant distributions.