Euihun Joung (Kyung Hee University) donnera le séminaire suivant dans la salle de réunion du Département de Physique au premier étage du bâtiment de Vinci :

Manifestly covariant worldline actions from coadjoint orbits

I will demonstrate how one can derive a manifestly covariant worldline action starting from Poincare and (A)dS algebra. Starting from a coadjoint orbit of the latter algebra and using the Kostant-Kirillov-Souriau symplectic structure on it, we first derive the unconstrained Hamiltonian action on a “curved » phase space, whose quantization would lead to a unitary irreducible representation of the starting Lie algebra. We then reformulate this action as a constrained Hamiltonian action on a “flat” embedding phase space. The set of constraints is in general a mixture of the first and second class constraints, and it defines a new coadjoint orbit of a “dual” symmetry. Upon quantization, this construction provides the reductive dual pair correspondence. I will also briefly comment about this correspondence, a very powerful tool to handle a large class of representations.