Penn Arts & Sciences Logo

Deformation Theory Seminar

Wednesday, January 28, 2004 - 1:45pm

Jae-Suk Park

CUNY

Location

University of Pennsylvania

DRL 4N30

Check hour closer to time

Exploiting the path integral approach al la Batalin and Vilkovisky, we show that any anomaly-free Quantum Field Theory (QFT) comes with a family parametrized by certain moduli space M, which tangent space at the point corresponding to the initial QFT is given by the space of all observables. Furthermore the tangent bundle over M is equipped with flat quantum connection, which can be used to determine all correlation functions of the family of QFTs. We also argue that considering family of QFTs is an inevitable step, due to the fact that the products of quantum observables are not quantum observables in general, which leads to a new "global" perspective on quantum world. We also uncover structure of d-algebra in the large class of d-dimensional QFT. This leads to an universal quantization machine for d-algebras decorated by algebro-differential-topology of (d+1)-manifolds as well as a new perspective on differential-topology of low dimensions.