Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

The aim of this talk is to show whether and how the space of solutions of the equations of motion of Hamiltonian field theories can be equipped with a Poisson structure. In particular, we will show how, in the multisympletic formalism, a canonical pre-symplectic structure on the space of solutions naturally emerges out of the principle of least action and, then, we ask whether and how such a pre-symplectic structure may give rise to a Poisson one. We will use the coisotropic embedding theorem to provide an answer to this question and we argue that in some cases it is possible to construct a Poisson structure directly on the space of solutions whereas in some situations one is forced to define it on an enlarged manifold. The guiding example we will consider along the talk, namely Yang-Mills theories, lies in the latter case and we will interpret the additional degrees of freedom emerging from the above mentioned enlargement as the ghost fields introduced in Quantum Field Theory by Fadeev and Popov.

If you want to join the seminar write to konieczn at fuw.edu.pl