Elements for Physics: Quantities, Qualities, and Intrinsic Theories
by Albert Tarantola
Publisher: Springer 2006
Number of pages: 280
The book reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented.
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by Marios Tsatsos - arXiv
The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can give rise to new descriptions of quantum physics.
by Arnold Neumaier, Dennis Westra - arXiv
This book presents classical, quantum, and statistical mechanics in an algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups.
by B. Eynard
This is an introductory course about random matrices. These notes will give the reader a smell of that fascinating tool for physicists and mathematicians that are Random Matrices, and they can give the envy to learn and search more.
by Pavel Bleher, Alexander Its - Cambridge University Press
The book covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.