دانلود کتاب فیزیک از طریق تقارن‌ها

For over a hundred years, group theory has played an essential role in theoretical physics. Even before that it was known that the solution of many mechanical systems (harmonic oscillator, Kepler problem) are possible because of symmetries. E. Noether showed that symmetries imply conservation laws in mechanics. Groupswere also useful in classifying periodic structures (crystals) and their X-ray diffraction patterns. Groups and their representation found its deepest uses in Quantum Theory. Wigner and Weyl were the pioneers. Groups served as a powerful tool to classify and understand particles and their states in nuclear and high energy physics. More fundamentally, interactions among elementary particles (electromagnetic and strong forces) turn out to be a consequence of non-abelian gauge symmetries. This idea has its roots in General Relativity, where Einstein found that general covariance leads to gravitational interactions. So you cannot understand modern theoretical physics without knowing some group theory. The field is too broad for one person to know everything about every group. Choices must be made. My choice of topics is admittedly personal. I have tried to emphasize the concepts (Lie theory, Peter-Weyl Theorem etc.) instead of techniques (listing of irreducible representations, calculation of Casimir invariants etc.). There are already excellent books that could train you in techniques. To say nothing of various online resources (Wikipedia, Scholarpedia etc.) that give a quick summary.Agood understanding can be obtained by studying a few representative cases in depth. Even if you encounter different cases in your own research, the knowledge so obtained can often be adapted. There are also indications that future physicists will need symmetries that go beyond groups. The most intriguing of these are “quantum groups”. So I have included them. I have tried to avoid symmetries that theorists love, but which have not found much experimental support. I wish there was time to do more. Among the omissions I regret most are: Coadjoint orbits, Virasoro and Kac-Moody algebras and Harish-Chandra’s theory of unitary representations of non-compact groups. The book is not meant to be read linearly, cover to cover. Several sections can be omitted in a first reading; they will make more sense when you return to them afterwards. They are denoted by a star in the section heading. The later chapters are more terse and technically involved. They can also be omitted in a first reading. The more examples and exercises you work out the better your understanding will be. Some of the exercises are solved in detail. But look at the solution only after a serious attempt. My own knowledge and appreciation of group theory is from my teacher, A. P. Balachandran; augmented by later interactions with Mark Bowick, Feza Gursey and Susumu Okubo. I owe a debt of gratitude also to Rakesh Tibrewala, who read most of the book with great care. His comments were very helpful. Of course, I own entirely any mistakes or confusions that remain. Thanks also to Christopher B Davis and Rhaimie BWahap ofWorld Scientific for their encouragement and patience through the slow process of writing the book.