With a symplectic manifold regarded as a classical mechanical. The geometric approach to quantization was introduced by konstant and souriau more than 20 years ago. Hamiltonian mechanical systems and geometric quantization. Geometric quantization in action download ebook pdf. Click download or read online button to get geometric quantization in action book now. Part of the encyclopaedia of mathematical sciences book series ems, volume 4. Kostants work has involved representation theory, lie groups, lie algebras, homogeneous spaces, differential geometry and mathematical physics, particularly symplectic geometry. If you are really mystified, you need to read some books on differential geometry and the math of classical mechanics before proceeding. The geometric approach to quantization was introduced by kostant and souriau more that twenty years ago.
Geometric quantization and quantum mechanics applied. Download pdf geometric quantization free online new. Geometric quantization and quantum mechanics jedrzej sniatycki. Symplectic manifold cotangent bundle geometric quantization. Czyz institute of mathematics, technical university, warsaw, poland received july 25. Geometric quantization pdf download top book edition. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as. The books of souriau 1970 and simms and woodhouse 1976 present the theory of geometric quantization and its relationship to quantum mech anics. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. Lectures on the geometry of quantization math berkeley.
This leads, in chapter 8, to topics such as foliated cohomology, the theory of the dolbeault kostant complex, and their applications. Geometric quantization over brst complexes is discussed in the following articles. Geometric quantization provides a way to pass between the geometric pictures of hamiltonian mechanics and the hilbert spaces of quantum mechanics. On geometric quantization and its connections with the. A discussion of the relation between geometric quantization and the marsdenweinstein reduction is presented in chapter 9. Geometric quantization is one formalization of the notion of quantization of a classical mechanical systemclassical field theory to a quantum mechanical systemquantum field theory. Quantization over a brst complex is hence quantization over an infinitesimal action groupoid. He has been one of the principal developers of the theory of geometric quantization. Souriau one of the initiators of the subject with bertram kostant in two texts essentially. This book contains a revised and expanded version of the lecture notes of two. It has given valuable and lasting insights into the.
In the book, the first reference, youll find the geometric prequantization. The geometric approach to quantization was introduced by kostant an. Geometric quantization pdf epub download cause of you. The word quantization is used both in physical and in mathematical works in many different senses. This leads, in chapter 8, to topics such as foliated cohomology, the theory of the dolbeaultkostant complex, and their applications. The book 29 treats further topics in symplectic geometry and mechanics, with special attention to the role of symmetry groups. In the early 1960s, kostant began to develop his method of coadjoint orbits and geometric quantization relating symplectic geometry to infinitedimensional representation theory.