Symplectic Geometry and Quantum Mechanics

• Symplectic Geometry.- Symplectic Spaces and Lagrangian Planes.- The Symplectic Group.- Multi-Oriented Symplectic Geometry.- Intersection Indices in Lag(n) and Sp(n).- Heisenberg Group, Weyl Calculus, and Metaplectic Representation.- Lagrangian Manifolds and Quantization.- Heisenberg Group and Weyl Operators.- The Metaplectic Group.- Quantum Mechanics in Phase Space.- The Uncertainty Principle.- The Density Operator.- A Phase Space Weyl Calculus.

From the reviews: "De Gosson's book is an exhaustive and clear description of almost all the more recent results obtained in connected areas of research like symplectiv geometry, the combinatorial theory of the Maslov index, the theory of the metaplectic group and so on. It fills an important niche in the literature." -Mircea Crasmareanu, Analele Stiintifice "This book concerns certain aspects of symplectic geometry and their application to quantum mechanics. ... This book seems best suited to someone who already has a solid background in quantum theory and wants to learn more about the symplectic geometric techniques used in quantization. ... the book contains useful information about various important topics." (Brian C. Hall, Mathematical Reviews, Issue 2007 e) "This book covers ... symplectic geometry and their applications in quantum mechanics with an emphasis on phase space methods. ... The exposition is very detailed and complete proofs are given. ... the book takes a particularly fresh point of view on some of the topics and contains a lot of useful information for readers with some background in quantum theory and an interest in the use of symplectic techniques." (R. Steinbauer, Monatshefte fur Mathematik, Vol. 155 (1), September, 2008)