algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
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 $d A = 0$, 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.
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.
Detailed review is in
Original articles include the following
Scott Axelrod, Isadore Singer, Chern-Simons Perturbation Theory, in S. Catto, A. Rocha (eds.) Proc. XXthe DGM Conf. World Scientific Singapore, 1992, 3-45; (arXiv:hep-th/9110056)
Scott Axelrod, Isadore Singer, Chern–Simons Perturbation Theory II, J. Diff. Geom. 39 (1994) 173-213 (arXiv:hep-th/9304087)
Raoul Bott, Alberto Cattaneo, Remark 3.6 in Integral invariants of 3-manifolds, J. Diff. Geom., 48 (1998) 91-133 (arXiv:dg-ga/9710001)
Alberto Cattaneo, Pavel Mnev, Remark 11 in Remarks on Chern-Simons invariants, Commun.Math.Phys.293:803-836,2010 (arXiv:0811.2045)
Maxim Kontsevich, Vassiliev’s knot invariants, Advances in Soviet Mathematics, Volume 16, Part 2, 1993 (pdf)
Maxim Kontsevich, pages 11-12 of Feynman diagrams and low-dimensional topology, First European Congress of Mathematics, 1992, Paris, vol. II, Progress in Mathematics 120, Birkhäuser (1994), 97–121 (pdf)
Pascal Lambrechts, Ismar Volić, sections 6 and 7 of Formality of the little N-disks operad, Memoirs of the American Mathematical Society ; no. 1079, 2014 (arXiv:0808.0457, doi:10.1090/memo/1079)
Alberto Cattaneo, Pavel Mnev, Nicolai Reshetikhin, appendix B of Perturbative quantum gauge theories on manifolds with boundary, Communications in Mathematical Physics, January 2018, Volume 357, Issue 2, pp 631–730 (arXiv:1507.01221, doi:10.1007/s00220-017-3031-6)
Ricardo Campos, Najib Idrissi, Pascal Lambrechts, Thomas Willwacher, Configuration Spaces of Manifolds with Boundary (arXiv:1802.00716)
Last revised on October 1, 2019 at 14:20:44. See the history of this page for a list of all contributions to it.