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AMS/IP Studies in Advanced Mathematics Geometric Analysis on the Heisenberg Group and Its GeneralizationsOriginal Publication: 1 January 2007 Publisher: American Mathematical Society / International Press Language: English Hardcover 244 pages List Price: $61.00 
Description
The book deals with the study of subRiemannian manifolds which have the Heisenberg principle built in. This brings the hope that Heisenberg manifolds (step 2 subRiemannain manifolds) will play a role in Quantum Mechanics in the future, similar to the role played by the Riemannian manifolds in Classical Mechanics.
The subRiemannian geodesics behavior, which is very different than in the Riemannian case, plays an important role in finding heat kernels and propagators for the Shrodinger’s equation, as well as in finding fundamental solutions for subelliptic operators using a very ingenious geometric method involving complex modified action.
One of the novelties of this book is to introduce the complex Hamiltonian mechanics techniques and apply them in describing the fundamental solutions and heat propagators. The fact that the propagator depends on each subRiemannian distance is an expected fact in Quantum Mechanics. The fact that each path has a contribution to the propagator led Feynman to introduce the path integrals. In this work we can manage without them, just working in the proper geometric framework.
This work is a text for a course or seminars designed for graduate students interested in the most recent developments in the subRiemannian manifolds and subelliptic operators theory. It is useful for both pure and applied mathematicians and theoretical physicists working in the quantum mechanics area.
This volume is part of the AMS/IP Studies in Advanced Mathematics book series.
Publications
Pub. Date 
ISBN13 
ISBN10 
Medium 
Binding 
Size, Etc. 
Status 
List Price 

2019 Apr 
9781470438296 
EBook 
In Print 

2016 Jan 
9780821846889 
0821846884 
paperback 
Out of Print 

2007 Jan 
9780821843192 
0821843192 
hardcover 
In Print 
US$61.00 