Even though touch geometry and topology is in short mentioned in V I Arnol'd's booklet "Mathematical equipment of Classical Mechanics "(Springer-Verlag, 1989, 2d edition), it nonetheless continues to be a website of study in natural arithmetic, e.g. see the new monograph by means of H Geiges "An creation to touch Topology" (Cambridge U Press, 2008). a few makes an attempt to exploit touch geometry in physics have been made within the monograph "Contact Geometry and Nonlinear Differential Equations" (Cambridge U Press, 2007). regrettably, even the superb type of this monograph isn't enough to draw the eye of the physics neighborhood to this kind of difficulties. This ebook is the 1st severe try to switch the prevailing established order. In it we exhibit that, actually, all branches of theoretical physics will be rewritten within the language of touch geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum pcs, and so on. The booklet is written within the kind of well-known Landau-Lifshitz (L-L) multivolume path in theoretical physics. which means its readers are anticipated to have stable history in theoretical physics (at least on the point of the L-L course). No past wisdom of specialised arithmetic is needed. All wanted new arithmetic is given within the context of mentioned actual difficulties. As within the L-L path a few problems/exercises are formulated alongside the way in which and, back as within the L-L direction, those are continuously supplemented by means of both strategies or by way of tricks (with distinctive references). in contrast to the L-L path, notwithstanding, a few definitions, theorems, and feedback also are provided. this is often performed with the aim of stimulating the curiosity of our readers in deeper examine of themes mentioned within the textual content.
Readership: Researchers and execs in utilized arithmetic and theoretical physics.