Quantum backgrounds and QFT

TL;DR

This paper introduces the concept of quantum backgrounds and a functor QFT, constructing a flat superconnection on the moduli space that encodes algebraic structures related to correlation functions in quantum field theory.

Contribution

It defines quantum backgrounds and functor QFT, and constructs a flat superconnection on the moduli space, providing a new algebraic framework for quantum field theories.

Findings

Constructed a flat quantum superconnection on the QFT moduli space.

Identified chain-level generalizations of correlation functions.

Provided a new algebraic structure relevant to quantum field theory.

Abstract

We introduce the concept of a quantum background and a functor QFT. In the case that the QFT moduli space is smooth formal, we construct a flat quantum superconnection on a bundle over QFT which defines algebraic structures relevant to correlation functions in quantum field theory. We go further and identify chain level generalizations of correlation functions which should be present in all quantum field theories.