Introduction To The Poisson Sigma Model, An

These lecture notes offer a general overview of a two-dimensional topological field theory called the Poisson Sigma Model. It is based on a series of talks given by the author at the University of California, Berkeley and the University of Massachusetts, Amherst in the fall of 2018 and the spring of 2019.This book contains an introduction to symplectic, Poisson and graded geometry, the path space construction for Lie algebroids via the reduced phase space of the Poisson Sigma Model, and the Cattaneo-Felder interpretation of Kontsevich's star product via Feynman diagrams. It also describes in detail particular cases of the Poisson Sigma Model, including constant, linear (2-dimensional BF-theory) and quadratic Poisson structures.The target audience of this book is graduate students and researchers with an interest in the mathematical aspects of classical and quantum field theory. No prior exposure to physics or Poisson geometry is required.