681 research outputs found
Symplectic areas, quantization, and dynamics in electromagnetic fields
A gauge invariant quantization in a closed integral form is developed over a
linear phase space endowed with an inhomogeneous Faraday electromagnetic
tensor. An analog of the Groenewold product formula (corresponding to Weyl
ordering) is obtained via a membrane magnetic area, and extended to the product
of N symbols. The problem of ordering in quantization is related to different
configurations of membranes: a choice of configuration determines a phase
factor that fixes the ordering and controls a symplectic groupoid structure on
the secondary phase space. A gauge invariant solution of the quantum evolution
problem for a charged particle in an electromagnetic field is represented in an
exact continual form and in the semiclassical approximation via the area of
dynamical membranes.Comment: 39 pages, 17 figure
Poisson sigma models and symplectic groupoids
We consider the Poisson sigma model associated to a Poisson manifold. The
perturbative quantization of this model yields the Kontsevich star product
formula. We study here the classical model in the Hamiltonian formalism. The
phase space is the space of leaves of a Hamiltonian foliation and has a natural
groupoid structure. If it is a manifold then it is a symplectic groupoid for
the given Poisson manifold. We study various families of examples. In
particular, a global symplectic groupoid for a general class of two-dimensional
Poisson domains is constructed.Comment: 34 page
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