Mathematical Physics Sector - G. Morchio 26/09 at 14.30 hrs.

[Barbara Corzani]

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MATHEMATICAL PHYSICS SEMINARS
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GIOVANNI MORCHIO 
(university of Pisa)

QUANTUM MECHANICS ON MANIFOLDS AND TOPOLOGICAL EFFECTS

Venue: September, Wed. 26, room D, 2,30 p.m.


Abstract: We will discuss the problem of constructing the one-particle
Quantum Mechanics on a manifold on the basis of the invariance under
diffeomorphisms. Algebraic Lie-Rinehart relations, expressing the
structure of module of vector fields on C-infinity functions, allow to
construct a unique C* algebra of observables, which is invariant under
diffeomorphisms, and "with no additional degrees of freedom". Its
representations, which are differentiable in the diffeomorphism
parameters, are all locally quasi-equivalent to the Schroedinger
representation, and are classified by the unitary representations of the
fundamental group of the manifold. Reference: G.Morchio, F.Strocchi,
arXiv 0707.3357