This book gives a presentday account of marston morse s theory of the calculus of variations in the large. Morse theory is a beautiful and natural extension of the minimum principle. Supersymmetry generators have speci c commutation properties with other generators. Lectures on morse theory, old and new morse theory is. In chapter 1 we introduce the basic notions of the theory and we describe the main properties of morse functions.
Morse was on the faculty of the institute for advanced study, and princeton. Morse theory, that may be applied to any simplicial complex or more. Bott, morse theory and its application to homotopy theory. We discuss a pl analogue of morse theory for pl manifolds. In a theory where supersymmetry is realized, each oneparticle state has at least a superpartner.
Division algebras and supersymmetry ii baez, john c. There are several notions of regular and critical points. Aithchison, supersymmetry in particle physics, cambridge university press is super clear and basic. Division algebras and supersymmetry iii huerta, john, advances in theoretical and mathematical physics, 2012.
Therefore, in a susy world, instead of single particle states, one has to deal with supermultiplets of particle states. In another context, a morse function can also mean an. Here is a more detailed presentation of the contents. Morse theory and floer homology michele audin springer. For a colorful history of morse theory and the events leading up to wittens paper, we highly recommend reading raoul botts recollections in 8. An introduction to morse theory translations of mathematical monographs yukio matsumoto isbn. Supersymmetry and morse theory 665 the results of 2 have an analogue for complex manifolds, which will be discussed in a separate paper. However, there have been important developments during the past few years which are not mentioned. Wess and bagger, supersymmetry and supergravity, princeton university pub. Since each pendulum is free to rotate 360 degrees,its configuration space is a. Morse theory the simplest example of supersymmetric quantum mechanics is a system which is very well known in mathematics. In this thesis, the profound connection between morse theory and supersymmetry will be explored along the lines of wittens 1982 paper. An introduction to morse theory translations of mathematical.
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