Lie Groups

Lie Groups
Author:
Publisher:
Total Pages: 296
Release: 1986
Genre: Lie groups
ISBN:

Geometric Quantization in Action

Geometric Quantization in Action
Author: N.E. Hurt
Publisher: Springer Science & Business Media
Total Pages: 362
Release: 1982-12-31
Genre: Mathematics
ISBN: 9789027714268

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.

Geometric Quantization in Action

Geometric Quantization in Action
Author: N.E. Hurt
Publisher: Springer Science & Business Media
Total Pages: 351
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400969635

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.

Harmonic Analysis on Symmetric Spaces and Applications I

Harmonic Analysis on Symmetric Spaces and Applications I
Author: Audrey Terras
Publisher: Springer Science & Business Media
Total Pages: 353
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461251281

Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.

Mathematical Theory of Feynman Path Integrals

Mathematical Theory of Feynman Path Integrals
Author: Sergio Albeverio
Publisher: Springer Science & Business Media
Total Pages: 184
Release: 2008-05-30
Genre: Mathematics
ISBN: 3540769544

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

First Workshop on Grand Unification

First Workshop on Grand Unification
Author: FRAMPTON
Publisher: Springer Science & Business Media
Total Pages: 366
Release: 2012-12-06
Genre: Science
ISBN: 1468469037

This workshop held at the New England Center provided a timely opportunity for over 100 participants to gather in a unique environment and discuss the present status of the unification of strong and electroweak forces. One reason for the timeliness was perhaps that experiments of the seventies had already lent confirmation to the separate theories of strong and of electroweak forces, so that for the eighties it now seems especially compelling to attempt the grand unification of these two forces. Also, the planned experiments to search for proton decay and the new experiments which are suggestive, though not yet conclusive, of non-zero neutrino rest masses add further stimulus to the theory. Thus, the workshop provided an ideal forum for exchange of ideas amongst active physicists. The presentations at the workshop covered the present status of both theory and experiment with a strong interplay. Also, there were presentations from the discipline of astrophysics which is becoming very intertwined with that of high-energy physics especially when in the latter one is addressing energies and temperatures that were extant only in the first nanosecond of the universe. On experiment, we heard a comprehensive coverage of the four United States proton decay experiments. The Brookhaven-Irvine-Michigan experiment in the Morton Salt Mine at Fairport Harbor, Ohio was discussed by LARRY SULAK, while DAVID WINN talked on the Harvard-Purdue-Wisconsin effort in the Silver King Mine, Utah. MARVIN MARSHAK and RICHARD STEINBERG described respectively the Soudan Mine, Minnesot~ and the Homestake Mine, South Dakot~experiments.

Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane

Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane
Author: Audrey Terras
Publisher: Springer Science & Business Media
Total Pages: 430
Release: 2013-09-12
Genre: Mathematics
ISBN: 146147972X

This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups Γ, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.