Morse theory, that may be applied to any simplicial complex or more. Supersymmetry generators have speci c commutation properties with other generators. Here is a more detailed presentation of the contents. Since each pendulum is free to rotate 360 degrees,its configuration space is a. In a theory where supersymmetry is realized, each oneparticle state has at least a superpartner. Division algebras and supersymmetry iii huerta, john, advances in theoretical and mathematical physics, 2012. Morse theory and floer homology michele audin springer. In this thesis, the profound connection between morse theory and supersymmetry will be explored along the lines of wittens 1982 paper. In chapter 1 we introduce the basic notions of the theory and we describe the main properties of morse functions.
Morse theory is a beautiful and natural extension of the minimum principle. Aithchison, supersymmetry in particle physics, cambridge university press is super clear and basic. This book gives a presentday account of marston morse s theory of the calculus of variations in the large. Wess and bagger, supersymmetry and supergravity, princeton university pub. An introduction to morse theory translations of mathematical monographs yukio matsumoto isbn. Lectures on morse theory, old and new morse theory is. 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. Bott, morse theory and its application to homotopy theory.
There are several notions of regular and critical points. Morse theory the simplest example of supersymmetric quantum mechanics is a system which is very well known in mathematics. Division algebras and supersymmetry ii baez, john c. An introduction to morse theory translations of mathematical.594 517 310 484 1428 1032 435 419 1128 1374 1471 829 1283 970 1495 12 1200 176 1445 217 1526 1454 300 386 869 490 313 1118 671 984 1296 213 152 425 121 1239