Geometry and Mathematical Physics Seminar 2011/2012

Thursday 16 February 2012. The Frank Adams Room (Room 1.212), the Alan Turing Building. 3pm

Quantization and Full Symbol Calculus on Lie Algebroids

Adam Biggs (University of Manchester)

We shall outline a method of quantization which in principle considers replacing graded algebras by suitable filtered algebra via full symbol calculus - this process has its motivation in deformation quantization where we consider a new multiplication up to $O(h)$. In particular we shall calculate the equivalence classes when we have a Lie algebroid $E$, and focus on the case of $TM$, with the trivial structure, and $T^*M$ with the structure induced from a Poisson manifold $M$.

Time permitting we shall then explain how this can be extended to the algebra of densities on a manifold for the cotangent bundle, and outline methods to introduce formal parameters into the setup.