E-Book Content
GREEN’S FUNCTIONS AND ORDERED EXPONENTIALS This book presents a functional approach to the construction, use and approximation of Green’s functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. In addition, it deals with adiabatic and stochastic approximations to unitary ordered exponentials. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics. h. m. f ri ed received his PhD from Stanford University in 1957. He spent a post-doctoral year at the Ecole Normale Sup´erieure in Paris and then three years teaching physics at UCLA. This was followed by a year as a visiting member of the Institute of Advanced Study in Princeton, and two years as a visiting physicist at the Courant Institute at NYU, before joining the Physics Department at Brown University. Professor Fried has lectured and performed research in university departments and institutes throughout the world, principally in Paris, Marseille and Nice, and is a Director of the Workshops on Non-Perturbative QCD, which alternate between the American University of Paris and La Citadelle, Villefranche-sur-Mer. He is now Professor Emeritus of Physic