Applications of Contact Geometry and Topology in Physics by Arkady L Kholodenko

By Arkady L Kholodenko

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 analysis in natural arithmetic, e.g. see the hot monograph via H Geiges "An advent to touch Topology" (Cambridge U Press, 2008). a few makes an attempt to take advantage of touch geometry in physics have been made within the monograph "Contact Geometry and Nonlinear Differential Equations" (Cambridge U Press, 2007). regrettably, even the superb variety of this monograph isn't enough to draw the eye of the physics group to this sort of difficulties. This booklet is the 1st critical try and swap the prevailing establishment. In it we display that, in reality, 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 forth. The booklet is written within the type of well-known Landau-Lifshitz (L-L) multivolume direction in theoretical physics. which means its readers are anticipated to have reliable heritage 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 direction a few problems/exercises are formulated alongside the way in which and, back as within the L-L direction, those are continuously supplemented by way of both suggestions or by means of tricks (with detailed references). in contrast to the L-L direction, although, a few definitions, theorems, and feedback also are offered. this can be performed with the aim of stimulating the curiosity of our readers in deeper examine of topics mentioned within the textual content.

Readership: Researchers and pros in utilized arithmetic and theoretical physics.

Show description

Read Online or Download Applications of Contact Geometry and Topology in Physics PDF

Best topology books


Even though the hunt for strong selectors dates again to the early 20th century, selectors play an more and more vital position in present study. This booklet is the 1st to gather the scattered literature right into a coherent and stylish presentation of what's recognized and confirmed approximately selectors--and what is still came upon.

From Topology to Computation: Proceedings of the Smalefest

A rare mathematical convention used to be held 5-9 August 1990 on the college of California at Berkeley: From Topology to Computation: harmony and variety within the Mathematical Sciences a global examine convention in Honor of Stephen Smale's sixtieth Birthday the themes of the convention have been a number of the fields within which Smale has labored: • Differential Topology • Mathematical Economics • Dynamical structures • conception of Computation • Nonlinear useful research • actual and organic functions This publication includes the lawsuits of that convention.

Applications of Contact Geometry and Topology in Physics

Even supposing touch geometry and topology is in brief mentioned in V I Arnol'd's ebook "Mathematical tools of Classical Mechanics "(Springer-Verlag, 1989, second edition), it nonetheless is still a site of study in natural arithmetic, e. g. see the hot monograph through H Geiges "An creation to touch Topology" (Cambridge U Press, 2008).

Why Prove it Again?: Alternative Proofs in Mathematical Practice

This monograph considers a number of famous mathematical theorems and asks the query, “Why turn out it back? ” whereas studying substitute proofs. It explores the several rationales mathematicians could have for pursuing and proposing new proofs of formerly proven effects, in addition to how they pass judgement on no matter if proofs of a given outcome are diversified.

Additional info for Applications of Contact Geometry and Topology in Physics

Sample text

The simplest knot with considerable symmetry, the figure eight knot, made of piece of springy wire may have selfintersection points. Langer and Singer conjectured that there should be at least three such points (counting multiplicity) in a knotted wire. 2. Recall that the knot K is a torus knot if it can be embedded into the surface of a torus [36]. 3. Based on the above facts it remains to connect solutions of the L-L Eq. 1. In order to place such solutions onto the Maxwellian tori. The above self-intersection conjecture has been analyzed further in a number of papers.

5) with ±κα replaced by −δ −2 . That is we re-obtain Eq. 3) in which −α2 is replaced by −δ −2 . The functional, Eq. 3), can be looked upon as time-independent version of the so-called Proca functional describing the massive Abelian gauge vector field [95]. 4) FG-L [ψ, A] = where the tensor F µν = ∂ µ Aν − ∂ ν Aµ , and its dual F˜ µν is ∗F µν = 12 εµνρσ Fρσ . j ν is the four-dimensional current j = (ρ, j). 5) March 19, 2013 10:56 9in x 6in Applications of Contact Geometry and Topology in Physics All About and Around Woltjer’s Theorem b1524-ch03 41 where is the d’Alambertian, that is = ∂t2 − ∇2 .

B1524-ch03 29 (b) Two types of Hopf links: (a) the right-hand Hopf link, (b) the left-hand Hopf link. The thickening of tubes can continue only till they reach the configuration when the cross-section of one tube will be tightly bounded by another torus tube and vice versa. This configuration bounds the energy from below. These arguments bring us to the necessity of introducing the volumes Vi of tubes for each link component. Without loss of generality, it is then possible to focus attention only at one knotted torus.

Download PDF sample

Rated 4.25 of 5 – based on 31 votes