Mathematical Methods of Physics
Publisher: Wikibooks 2017
Number of pages: 98
Mathematical methods of Physics is a book on common techniques of applied mathematics that are often used in theoretical physics. It may be accessible to anyone with beginning undergraduate training in mathematics and physics. It will be useful for anyone wishing to study advanced Physics.
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by Peter B. Gilkey - Publish or Perish Inc.
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas and the Gauss-Bonnet theorem.
by Leonard Susskind - arXiv.org
The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes...
by A. Goetschy, S.E. Skipetrov - arXiv
We review the state of the art of the theory of Euclidean random matrices, focusing on the density of their eigenvalues. Both Hermitian and non-Hermitian matrices are considered and links with simpler random matrix ensembles are established.
by Nicolas Raymond - arXiv
'Little Magnetic Book' is devoted to the spectral analysis of the magnetic Laplacian in various geometric situations. In particular the influence of the geometry on the discrete spectrum is analysed in many asymptotic regimes.