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 Poisson algebras internal to graded vector spaces (such as Gerstenhaber algebras):
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
Alberto S. Cattaneo, Pavel Mnev, Michele Schiavina, BV Quantization, Encyclopedia of Mathematical Physics 2nd ed [arXiv:2307.07761]
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]
Giovanni Canepa, Alberto Cattaneo, Corner Structure of Four-Dimensional General Relativity in the Coframe Formalism, Annales Henri Poincaré 25 (2024) 2585–2639 [arXiv:2202.08684, doi:10.1007/s00023-023-01360-8]
Alberto S. Cattaneo, Phase space for gravity with boundaries, in Encyclopedia of Mathematical Physics 2nd ed (2023) [arXiv:2307.04666]
and for flux observables:
and relation to BF-theory:
On the relativistic particle, and related systems, in BV-BRST formalism:
On boundary field theory and the standard model of particle physics coupled to gravity:
On forumating D=3 supergravity in BV-formalism and relation to AKSZ theory:
Last revised on December 20, 2024 at 10:46:31. See the history of this page for a list of all contributions to it.