الصفحة 1
الصفحة 1
Mathematical Theory of Feynman Path Integrals : An Introduction
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory.
Braid Groups
Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups.
