Celebratio Mathematica

A. Connes and A. Schwarz: “Matrix Vieta theorem revisited,” Lett. Math. Phys. 39 : 4 (1997), pp. 349–353. MR 1449580 Zbl 0874.15010 article

A. Connes, M. R. Douglas, and A. Schwarz: “Noncommutative geometry and matrix theory: Compactification on tori,” J. High Energy Phys. 1998 : 2 (1998). article no. 3, 35 pages. MR 1613978 Zbl 1018.81052 ArXiv hep-th/9711162 article

Alain Connes	Related
Michael R. Douglas	Related

A. Schwarz: “Symplectic formalism in conformal field theory,” pp. 957–977 in Symétries quantiques / Quantum symmetries (Les Houches, France, 1 August–8 September 1995). Edited by A. Connes, K. Gaweedzki, and J. Zinn-Justin. Elsevier (Amsterdam), 1998. MR 1616364 Zbl 1050.81061 incollection

Jean Zinn-Justin	Related
Alain Connes	Related
Krzysztof Gawędzki	Related

A. Schwarz: “Noncommutative supergeometry, duality and deformations,” Nuclear Phys. B 650 : 3 (2003), pp. 475–496. To Alain Connes on his 55th birthday. MR 1952770 Zbl 1006.81083 ArXiv hep-th/0210271 article

Following Lett. Math. Phys. 50 (1999) 309, we introduce a notion of \( \mathcal{Q} \)-algebra that can be considered as a generalization of the notion of \( \mathcal{Q} \)-manifold (a supermanifold equipped with an odd vector field obeying \( \{Q,Q\} = 0 \)). We develop the theory of connections on modules over \( \mathcal{Q} \)-algebras and prove a general duality theorem for gauge theories on such modules. This theorem containing as a simplest case \( SO(d,d,\mathbb{Z}) \)-duality of gauge theories on noncommutative tori can be applied also in more complicated situations. We show that \( \mathcal{Q} \)-algebras appear naturally in Fedosov construction of formal deformation of commutative algebras of functions and that similar \( \mathcal{Q} \)-algebras can be constructed also in the case when the deformation parameter is not formal.

year	title	people

			clear

Albert S. Schwarz

Complete Bibliography

Works connected to Alain Connes

Filter the Bibliography List