More transition amplitudes on the Riemann sphere

TL;DR

This paper demonstrates that correlation functions in a bosonic conformal field theory on the Riemann sphere can be interpreted as transition amplitudes, establishing a connection between functional integrals and Hilbert space operators.

Contribution

It shows that correlation functions in this setting define multilinear Hilbert-Schmidt functionals, linking conformal field theory correlation functions to transition amplitudes.

Findings

Correlation functions are singular limits of functional integrals.

Correlation functions define multilinear Hilbert-Schmidt functionals.

Transition amplitudes are realized as these functionals on a fixed Hilbert space.

Abstract

We consider a conformal field theory for bosons on the Riemann sphere. Correlation functions are defined as singular limits of functional integrals. The main result is that these amplitudes define transition amplitudes, that is multilinear Hilbert-Schmidt functionals on a fixed Hilbert space.