nLab Alberto Cattaneo

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• publication list: pdf

Selected writings

On 3-manifolds:

• Raoul Bott, Alberto Cattaneo, Integral Invariants of 3-Manifolds, J. Diff. Geom., 48 (1998) 91-133 (arXiv:dg-ga/9710001)

On deformation quantization:

• Alberto Cattaneo, From topological field theory to deformation quantization and reduction, ICM 2006. (pdf)

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)

  math.SG/0003023.

• 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):

• Alberto Cattaneo, Pavel Mnev, Nicolai Reshetikhin, Classical BV theories on manifolds with boundary, arXiv:1201.0290; Classical and quantum Lagrangian field theories with boundary, arXiv:1207.0239; Perturbative quantum gauge theories on manifolds with boundary, arxiv/1507.01221

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]

Related $n$Lab entries

• Poisson sigma-model

• deformation quantization

• BV-quantization

• first-order formulation of gravity