This work aims to illuminate the relations between quantum and classical mechanics. There is some discussion of philosophical matters such as measurement, uncertainty, and decoherence, for example, but this is not emphasized; generally the text presents the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1, connections of QM to deterministic behaviour are exhibited in the trajectory representations of Faraggi-Matone, and there is a review of KP theory and some preliminary remarks on coherent states, and related topics. Chapter 2 studies the QM of embedded curves and surfaces, illustrating some QM effects of geometry, while Chapter 3 examines quantum integrable systems, quantum groups, and modern deformation quantization. Further chapters involve, for example, the Whitham equations in various roles, mediating between QM and classical behaviour. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed. There is also some conceptual background for such areas as susy, gauge theories, and renormalization, from both a physical and mathematical point of view.
- ISBN10 1281036269
- ISBN13 9781281036261
- Publish Date 1 January 2000
- Publish Status Active
- Out of Print 17 June 2015
- Publish Country US
- Imprint North-Holland
- Format eBook
- Pages 407
- Language English