دانلود کتاب هندسه دیفرانسیل و نظریه گروه‌ها

Differential geometry and group theory are the two pillars of geometry upon which the whole edifice of modern physics rests. Any serious theoretical physicist must be able to master these techniques, regardless of their field of specialization. There are plenty of textbooks on mathematical methods for physics, and many textbooks on group theory and differential geometry. The vast majority of them are plagued by abstract formalism, which obscures the mental visualization of geometric concepts. In other words, most books available on this subject do not offer the kind of physical intuition without which the learner cannot achieve an in- depth, working understanding of tools that are essential for physical scientists at all levels. Historically, this state of affairs is largely a product of the supremacy of the abstract style in teaching mathematics introduced by the Bourbaki school around the middle of the last century. The contagion of the Bourbaki style has spread widely outside pure mathematics and has partly infected several schools of mathematical and theoretical physics. This problem had already been stigmatized by Yakov B. Zeldovich, one of the greatest physicists in the second half of the twentieth century, who emphasized the damage that Bourbaki-style formalism can do to physics students. Captivated by the elegance of formalism, many of them are often unable to correctly visualize the underlying notions and objects, which are instead always connected, in some way, to our empirical representation of space. As emphasized by Zeldovich, for example in the prefaces to his own books of mathematical methods, Higher Mathematics for Beginners (with I.M. Yaglom) and Elements of Applied Mathematics (with A.D. Myskis), this tendency toward abstract formalism has catastrophic consequences for many (though of course not all) learners of theoretical physics and has produced legions of theorists with little physical intuition about the real world. In the same spirit of Zeldovich, whose papers and books have greatly influenced my own work and approach to physics, the present textbook attempts to provide an anti-Bourbakist, accessible path for future scientists and engineers (including beginners) to penetrate the world of advanced geometry and its applications to physical problems