Geometric Analysis on the Heisenberg Group and Its Generalizations [Kietas viršelis]

Although designed as a course or seminar text for graduate students interested in developments in the subReimannian manifolds (manifolds with the Heisenberg principle built in) and sub-elliptic operators theory, this also works as a resource for pure and applied mathematicians and theoretical physics working in quantum mechanics. One of the authors' most interesting innovations is introducing the complex Hamiltonian mechanics techniques and use them to describe the fundamental solutions and heat propagators in quantum mechanics. They introduce geometric mechanics on the Heisenberg group, then give geometric analyses of the step 4 case, the step 2(k+1) case, the geometry of higher dimensional Heisenberg groups, complex Hamiltonian mechanics and quantum mechanics on the Hiesenberg group. The result is fresh and lively while also being thorough. The authors provide exercises for each chapter. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)