Riferimento

This is one of the most popular graduate-level mathematical physics textbooks along with Arfken’s book. As of the latest edition, the 2nd edition introduced hereby, Clifford algebra and expression theory have been added, and the explanation of the mathematical foundations of differential manifolds, fiber bundles, and gauge theory, starting with tensor analysis is contained in the book in the most detail manner than any other textbooks.

The first part deals with linear algebra as an introduction to abstract algebra. Not only does it rigorously introduce mathematical theories, but it also does not miss practical calculation methods in physics. Afterward, the basics of functional analysis are briefly covered, and then the classification of differential equations and solution series in physics, Fourier transform, and complex analysis will be covered in depth. Integral transformation and integral equations are covered in one chapter each, and Green’s function, which spans three chapters, can be said to be the highlight of the first half of mathematical physics. In the case of finite group theory, it is covered in several times more detail and rigor than Arfken.

In addition, several chapters are devoted to explaining representation theory, and there are very detailed and application-oriented examples, providing a foundation for a solid understanding of quantum mechanics for undergraduate students and above.

The expression of Lie group and Lie algebra is also covered in detail. The symmetry of a system of differential equations through the application of Lie group and Lie algebra is explained over two chapters, and the complete explanation of Noether’s theorem at the end is the highlight. The last part is a thorough introduction to differential geometry and Riemannian geometry based on bundle theory.

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