دانلود کتاب Group Theory and Its Applications

From the Preface:The importance of group theory and its utility in applications to variousbranches of physics and chemistry is now so well established and universallyrecognized that its explicit use needs neither apology nor justification. Mattershave moved a long way since the time, just thirty years ago, when Condon andShortley, in the introduction to their famous book, "The Theory of AtomicSpectra", justified their doing "group theory without group theory" by thestatement that "... the theory of groups ... is not . . . part of the ordinarymathematical equipment of physicists." The somewhat adverse, or at leastsceptical, attitude toward group theory illustrated by the telling there of thewell-known anecdote concerning the Weyl-Dirac exchange,* has been replacedby an uninhibited and enthusiastic espousal. This is apparent from thesteadily increasing number of excellent textbooks published in this fieldthat seek to instruct ever widening audiences in the nature and use of thistool. There is, however, a gap between the material treated there and theresearch literature and it is this gap that the present treatise is designed to fill.The articles, by noted workers in the various areas of group theory, each reviewa substantial field and bring the reader from the level of a general understandingof the subject to that of the more advanced literature.The serious student and beginning research worker in a particular branchshould find the article or articles in his specialty very helpful in acquaintinghim with the background and literature and bringing him up to the frontiersof current research; indeed, even the seasoned specialist in a particular branchwill still learn something new. The editor hopes also to have the treatise serveanother useful function: to entice the specialist in one area into becomingacquainted with another. Such ventures into novel fields might be facilitatedby the recognition that similar basic techniques are applied throughout; e.g.,the use of the Wigner-Eckart theorem can be recognized as a unifying threadrunning through much of the treatise.The applications of group theory can be subdivided generally into twobroad areas: one, where the underlying dynamical laws (of interactions) andtherefore all the resulting symmetries are known exactly; the other, wherethese are as yet unknown and only the kinematical symmetries (i.e. those ofthe underlying space-time continuum) can serve as a certain guide.In the first area, group theoretical techniques are used essentially to exploitthe known symmetries, either to simplify numerical calculations or to drawexact, qualitative conclusions. All (extra-nuclear) atomic and molecularphenomena are believed to belong to this category; the central chapters inthis book deal with such applications, which, until relatively recently, formedthe bulk of all uses of group theory.In the second major area, application of group theory proceeds essentiallyin the opposite direction: It is used to discover as much as possible of theunderlying symmetries and, through them, learn about the physical laws ofinteraction. This area, which includes all aspects of nuclear structure andelementary particle theory, has mushroomed in importance and volume ofresearch to an extraordinary degree in recent times; the articles in the secondhalf of the treatise are devoted to it.I n part as a consequence of these developments, physical scientists havebeen forced to concern themselves more profoundly with mathematicalaspects of the theory of groups that previously could be left aside; questionsof topology, representations of noncompact groups, more powerful methodsfor generating representations as well as a systematic study of Lie groups andtheir algebras in general belong in this category. They are treated in theearlier chapters of this book.Considerations of both space and timing have forced omission from thisvolume of articles dealing with several important areas of applied group theorylike molecular spectra, hidden symmetry and "accidental" degeneracy, grouptheory and computers, and others. These will be included in a second volume,currently in preparation.Complete uniformity and consistency of notation is an ideal to be strivenfor but difficult to attain; it is especially hard to achieve when, as in the presentcase, many different and widely separated specialities are discussed, each ofwhich usually has a well-established notational system of its own which maynot be reconcilable with an equally well-established one in another area. Inthe present book uniformity has been carried as far as possible, subject tothese restrictions, except where it would impair clarity.