|Date||May 20, 2016|
Iterated path integrals, generalising the familiar line integrals, are functions in the path space of smooth manifold which notion has introduced and used to extend de Rham cohomology theory to a homotopy theory on the fundamental group level by by K.-T. Chen. The theory has found many interesting applications, beyond algebraic topology, in algebraic geometry and number theory. Theory of homotopy category of homotopy QFT algebras is this speaker’s attempts to understand quantum field theory mathematically. In this lecture I will show that iterated integral(s) is quantum expectation of a (0+0)-dimensional non-commutative QFT obtained by certain quantisation of the algebra of differential forms on a manifold such that Chen’s homotopy functionals are equivalent to quantum correlation functions. Both Chen’s theory and NC QFT theory will be introduced beforehand.