nLab
Chern-Simons propagator

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

The Chern-Simons propagator is the Feynman propagator for Chern-Simons theory regarded as a Euclidean quantum field theory. Since the Feynman propagator only depends on the free field theory-equations of motion (the staring point of perturbative QFT), which here is dA=0d A = 0, its form is independent of the gauge group and in fact applies also to all higher Chern-Simons theories such as notably the AKSZ sigma-models.

In the perturbative quantization of 3d Chern-Simons theory the CS propagator was first studied in Axelrod-Singer 91.

As a smooth differential form on compactified configuration spaces

The Chern-Simons propagator was re-formulated as a smooth differential form on compactified configuration space in Axelrod-Singer 93, p. 5-6. In this specific form its mathematical nature was amplified in Bott-Cattaneo 97, remark 3.6 and Cattaneo-Mnev 10, Remark 11. It was suggested that this serves to exhibit its Feynman amplitudes as exhibiting a graph complex-model for the de Rham cohomology of configuration spaces of points in Kontsevich 93, Kontsevich 94, which was proven in Lambrechts-Volic 14. This role of the Chern-Simons propagator is advertized also in Campos-Idrissi-Lambrechts-Willwacher 18, p. 66.

References

Detailed review is in

  • Konstantin Wernli, section 3 of Perturbative Quantization of Split Chern-Simons Theory on Handlebodies and Lens Spaces by the BV-BFV formalism, 2018

Original articles include the following

Last revised on October 1, 2019 at 10:20:44. See the history of this page for a list of all contributions to it.