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Although contact geometry and topology is briefly discussed in V I
Arnol'd's book "Mathematical Methods of Classical Mechanics
"(Springer-Verlag, 1989, 2nd edition), it still remains a domain of
research in pure mathematics, e.g. see the recent monograph by H
Geiges "An Introduction to Contact Topology" (Cambridge U Press,
2008). Some attempts to use contact geometry in physics were made
in the monograph "Contact Geometry and Nonlinear Differential
Equations" (Cambridge U Press, 2007). Unfortunately, even the
excellent style of this monograph is not sufficient to attract the
attention of the physics community to this type of problems. This
book is the first serious attempt to change the existing status
quo. In it we demonstrate that, in fact, all branches of
theoretical physics can be rewritten in the language of contact
geometry and topology: from mechanics, thermodynamics and
electrodynamics to optics, gauge fields and gravity; from physics
of liquid crystals to quantum mechanics and quantum computers, etc.
The book is written in the style of famous Landau-Lifshitz (L-L)
multivolume course in theoretical physics. This means that its
readers are expected to have solid background in theoretical
physics (at least at the level of the L-L course). No prior
knowledge of specialized mathematics is required. All needed new
mathematics is given in the context of discussed physical problems.
As in the L-L course some problems/exercises are formulated along
the way and, again as in the L-L course, these are always
supplemented by either solutions or by hints (with exact
references). Unlike the L-L course, though, some definitions,
theorems, and remarks are also presented. This is done with the
purpose of stimulating the interest of our readers in deeper study
of subject matters discussed in the text.
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