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This book is intended as a fairly complete presentation of what··'We call the discretization approach to functional integrals, i.e. path integrals defined as limits of discretized axpressions. In its main parts it is based 0n the original work of the authors. We hope to have provided the readers with a rather complete and up-to-date bibliography, and we apologize to authors whose work has not been cited through ignorance ori our part. Our main concern has been to present a for malism that is practical and which can be adapted to make computations in the numerous areas where path integrals are being increasingly used. For these reasons applications, illustrative examples, and detailed calculations are included. The book is partially based on lectures given by one of us (E.T.) at the Institut de Physique Theorique of the u.c.L. (Louvain-la-Neuve). We thank Dr. M.E. Brachet (University of Paris) for his help in the redaction of chapter 8. We are indebted to many of our colleagues and especially to the members of the Instituut voor Theoretische Fysica, K.U. Leuven for their interest and encouragement. We also thank Professor Claudio Anguita, Dean of the Faculty of Physics and Mathematics of .the University of Chile, for his constant support. Special thanks are due to Christine Detroije and Lutgarde Dubois for their very fine and hard work in typing the manuscript.
Table des matières
I: Functional integrals defined as limits of discretized expressions.- II: Correspondence rules and functional integral representations.- III: Functional integral representations of expectation values. Time-ordered products.- IV: Perturbation expansions.- V: Short time propagators and the relations between them.- VI: Covariant definitions of functional integrals.- VII: Functional integral methods in Fokker-Planck dynamics.- VIII: Product integrals.- IX: The semiclassical expansion in phase space.- X: The semiclassical expansion in configuration space.- XI: Other approaches.- XII: Computation of the propagator on the sphere S3.- References.
