by David Tong
Publisher: University of Cambridge 2005
Number of pages: 140
These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory. The lectures consist of four sections, each dealing with a different soliton.
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by C.L. Siegel - Tata Institute of Fundamental Research
From the table of contents: The differential equations of mechanics; The three-body problem : simple collisions (The n-body problem); The three-body problem: general collision (Stability theory of solutions of differential equations).
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The subject of these lecture notes is spectral theory of self-adjoint operators and some of its applications to mathematical physics. The main theme is the interplay between spectral theory of self-adjoint operators and classical harmonic analysis.
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The text deals with basic Group Theory and its applications. Contents: Abstract Group Theory; Theory of Group Representations; Group Theory in Quantum Mechanics; Lie Groups; Atomic Physics; The Group SU2: Isospin; The Point Groups; The Group SU3.
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.