On 3-manifolds:
On higher order Vassiliev invariants as Chern-Simons theory-correlators, hence as configuration space-integrals of wedge products of Chern-Simons propagators assigned to edges of Feynman diagrams in the graph complex:
Alberto Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni, Configuration spaces and Vassiliev classes in any dimension, Algebr. Geom. Topol. 2 (2002) 949-1000 (arXiv:math/9910139)
Alberto Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni, Algebraic structures on graph cohomology, Journal of Knot Theory and Its Ramifications, Vol. 14, No. 5 (2005) 627-640 (arXiv:math/0307218)
On the Poisson sigma-model:
Alberto Cattaneo, Giovanni Felder, A path integral approach to the Kontsevich quantization formula, Commun. Math. Phys. 212, 591–611 (2000) doi, math.QA/9902090.
Alberto Cattaneo, Giovanni Felder, Poisson sigma models and deformation quantization, Mod. Phys. Lett. A 16, 179–190 (2001) hep-th/0102208
Alberto Cattaneo, Giovanni Felder, Poisson sigma models and symplectic groupoids , (ed. Klaas Landsman, M. Pflaum, M. Schlichenmeier), Progress in Mathematics 198, 61–93 (Birkhäuser, 2001)
Alberto Cattaneo, Giovanni Felder, On the AKSZ formulation of the Poisson sigma model, Lett. Math. Phys. 56, 163–179 (2001) math.QA/0102108.
On BV-BRST formalism compatible with decomposing spacetime into pieces (BV-BFV formalism):
On the local formulation (allowing decomposition and re-gluing of spacetime) of the phase space of Einstein gravity in first-order formulation via BV-BFV formalism:
Alberto Cattaneo, Michele Schiavina, BV-BFV approach to General Relativity, Einstein-Hilbert action, J. Math. Phys. 57 023515 (2016) [arXiv:1509.05762, doi:10.1063/1.4941410]
Alberto Cattaneo, Michele Schiavina, The reduced phase space of Palatini-Cartan-Holst theory, Ann. Henri Poincaré 20 (2019) 445 [arXiv:1707.05351, doi:10.1007/s00023-018-0733-z]
Alberto Cattaneo, Michele Schiavina, BV-BFV approach to General Relativity: Palatini-Cartan-Holst action, Adv. Theor. Math. Phys. 23 (2019) 1801-1835 [arXiv:1707.06328, doi:10.4310/ATMP.2019.v23.n8.a3]
Alberto S. Cattaneo, Phase space for gravity with boundaries, Encyclopedia of Mathematical Physics (2023) [arXiv:2307.04666]
Last revised on July 13, 2023 at 11:58:40. See the history of this page for a list of all contributions to it.