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Lectures on the Geometry of Quantization
These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.
Loop Spaces, Characteristic Classes and Geometric Quantization
This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Lie Theory
* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.
Student’s Guide to Calculus by J. Marsden and A. Weinstein
This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book. (He was one of the best students that year, by the way. ) Because of his background, Fred has taken, in the Guide, the point of view of an experienced student tutor helping you to learn calculus. \~ile we do not always think Fred's jokes are as funny as he does, we appreciate his enthusiasm and his desire to enter into communication with his readers; since we nearly always agree with the mathe matical judgements he has made in explaining the material, we believe that this Guide can se...
Metric Structures for Riemannian and Non-Riemannian Spaces
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Wisdom From the Homeless
SOMETIMES THE WORLD SEEMS LIKE A VERY DARK PLACE. In this angry world, I have seen a glimpse of light. I have seen kindness, love and hope at a homeless shelter. Siloam Mission is named after a pool where, in Biblical times, Jesus healed a blind man. In this tradition, the Mission has a medical clinic, and I have had the privilege of working there. The homeless men and women I have met at Siloam have taught me profound lessons about perseverance through suffering, expressing joy in dire circumstances, and the rewards of service to those in need. I want to share those lessons with you.
Standoff at Christmas
DANGEROUS HOLIDAY HOMECOMING Anchorage K-9 officer Jake Nichols returns home for Christmas to recover from the accident that almost killed him--and find a little peace and quiet. But those plans are shattered when his childhood friend Rachel Hart gets caught up in a drug-smuggling ring after her aunt is brutally murdered. Jake quickly discovers that Port Aurora is no longer the tranquil little fishing town he left behind. He promises Rachel that he'll stick around until he tracks down the killer--and vows to protect her at all costs. Both of their lives are in peril as he battles against the Alaskan winter, a ruthless criminal...and his developing feelings for Rachel. Alaskan Search and Rescue: Risking their lives to save the day
Samantha's Gift
Though the gossips had them pegged as an item, teacher Rachel Woodward was merely helping Sean Bates, the new guidance counselor, learn small-town ways. But his looks and charm were almost irresistible. And it was a good thing Rachel no longer fell prey to romantic insanity. Yet she couldn’t ignore Sean, or how wonderfully he cared for the sweet, rambunctious five-year-old who’d landed in their school—and both their hearts. Little Samantha needed a father, and Sean would be the perfect man for the job. But she needed a mother, too...and suddenly Rachel wondered if God had a family in store for her after all.
Lie Groups Beyond an Introduction
This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.
