Principal Symbol on Contact Manifolds

We use the results of Chap. 3 to define the principal symbol mapping on contact manifolds. A significant application of this theory is a proof of a general version of Connes’ trace formula on contact manifolds. This version of Connes’ trace theorem is stated in terms of the Liouville trace on the group von Neumann algebra bundle, a non-commutative analogue of the Liouville measure on the cotangent bundle defined in Sect. 4.3.