Lectures on integrable hierarchies and vertex operators

Abstract

This is a write-up of lectures intended for (under)graduate students. Contents: Scalar Ansatz (KP hierarchy). Fermionic Fock space. Fermi-Bose correspondence. KP hierarchy via free fermions. Formal distributions and locality. Operator product expansion. Vertex algebras. Free fermions. Virasoro algebra in KdV.

AMSLaTeX, 28 pages. Lectures given at the 2004 DIAS-TH Winter school on theoretical physics in Dubna, Russia. Last updates and other lecture notes are available at http://thsun1.jinr.ru/~alvladim/qft.html