nLab Albert Schwarz

Albert Solomonowich Schwarz is a mathematician and a theoretical physicist born in Soviet Union and now Professor at University of California-Davis (web). He was one of the pioneers of Morse theory and brought up a first example of a topological quantum field theory. Schwarz worked on some examples in noncommutative geometry. He is “S” of the famous AKSZ model.

• personal page

• Wikipedia entry

• MathGenealogy entry

• inSpire page

• GoogleScholar page

• Albert Schwarz: My Life In Science (2004) [pdf, pdf]

Selected writings

(See also the list of arXiv articles of A. Schwarz.)

On general topology, homotopy theory and algebraic topology for application to topological quantum field theory and topological phases of matter:

• Albert S. Schwarz: Topology for Physicists, Grundlehren der mathematischen Wissenschaften 308, Springer (1994) [doi:10.1007/978-3-662-02998-5]

On noncommutative tori:

• Marc Rieffel, Albert Schwarz, Morita equivalence of multidimensional noncommutative tori, Int. J. Math. 10 (1999) 289-299 (arXiv:math/9803057)

On Morita equivalence and duality in physics/duality in string theory:

• Albert Schwarz, Morita equivalence and duality (arXiv:hep-th/9805034)

and specifically in relation to T-duality:

• B. Pioline, Albert Schwarz, Morita equivalence and T-duality (or $B$ versus $\Theta$) (arXiv:hep-th/9908019)

On partition functions

• Albert SchwarzThe partition function of a degenerate functional, Commun. Math. Phys. 67, 1 (1979)

Introducing the AKSZ sigma-model:

• M. Alexandrov, Maxim Kontsevich, Albert Schwarz, Oleg Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Modern Phys. A 12(7):1405–1429, 1997 (arXiv:hep-th/9502010)

On supergeometry as taking place over the base topos on the site of super points

• Albert Schwarz, On the definition of superspace, Teoret. Mat. Fiz. (1984) Volume 60, Number 1, Pages 37–42, (russian original pdf)

• Anatoly Konechny and Albert Schwarz,

  On $(k \oplus l|q)$-dimensional supermanifolds, in: Julius Wess, V. Akulov (eds.) Supersymmetry and Quantum Field Theory (D. Volkov memorial volume) Springer-Verlag, 1998 , Lecture Notes in Physics, 509 (arXiv:hep-th/9706003)

  Theory of $(k \oplus l|q)$-dimensional supermanifolds Sel. math., New ser. 6 (2000) 471 - 486

• Albert Schwarz, I- Shapiro, Supergeometry and Arithmetic Geometry (arXiv:hep-th/0605119)

On the Lie algebra cohomology of the super Poincaré Lie algebra (brane scan of Green-Schwarz sigma-models):

• Mikhail Movshev, Albert Schwarz, Renjun Xu, Homology of Lie algebra of supersymmetries (arXiv:1011.4731)

• Mikhail Movshev, Albert Schwarz, Renjun Xu, Homology of Lie algebra of supersymmetries and of super Poincaré Lie algebra, Nuclear Physics B Volume 854, Issue 2, 11 January 2012, Pages 483–503 (arXiv:1106.0335)

On D=10 super Yang-Mills theory:

• Mikhail Movshev, Albert Schwarz, On maximally supersymmetric Yang-Mills theories, Nucl.Phys. B681 (2004) 324-350 (arXiv:hep-th/0311132)

On supersymmetry and equivariant localization:

• Albert Schwarz, Oleg Zaboronsky, Supersymmetry and localization, Comm. Math. Phys. 183, 2 (1997), 463-476 (euclid:cmp/1158328185)

On BV-formalism

• Geometry of Batalin-Vilkovisky quantization, Commun. Math. Phys. 155, 249 (1993), euclid

On the semiclassical approximation in BV-formalism:

• Semiclassical approximation in Batalin-Vilkovisky formalism, Comm. Math. Phys. 158 (1993), no. 2, 373–396, euclid

On quantum field theory and topology:

• Albert Schwarz: Quantum Field Theory and Topology, Grundlehren der Math. Wissen. 307, Springer (1993) [doi:10.1007/978-3-662-02943-5]

See also:

• scientific reminiscences, pdf

• V. Kac, A. Schwarz, Geometric interpretation of the partition function of $2$D gravity, Phys. Lett. B 257 (1991), no. 3-4, 329–334, doi

• A. A. Belavin, A. M. Polyakov, A. S. Schwartz, Yu. S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. B 59 (1975), no. 1, 85–87, http://dx.doi.org/10.1016/0370-2693(75)90163-X

• S. N. Dolgikh, A. A. Rosly, A. S. Schwarz, Supermoduli spaces, Comm. Math. Phys. 135 (1990), no. 1, 91–100, euclid

• V. N. Romanov, A. S. Švarc, Anomalies and elliptic operators, (Russian) Teoret. Mat. Fiz. 41 (1979), no. 2, 190–204.

• Математические основы квантовой теории поля, Atomizdat, Moscow, 1975. 368 pp.

On 1-twisted de Rham cohomology:

• Albert Schwarz, Ilya Shapiro, Twisted de Rham cohomology, homological definition of the integral and “Physics over a ring”, Nucl. Phys. B 809 (2009) 547-560 [arXiv:0809.0086, [doi:10.1016/j.nuclphysb.2008.10.005]

On quantum mechanics and quantum field theory:

• Igor Frolov, Albert Schwarz, Quantum mechanics and quantum field theory. Algebraic and geometric approaches, lecture notes [arXiv:2301.03804]

On super Riemann surfaces and fat graphs:

• Albert S. Schwarz, Anton M. Zeitlin, Super Riemann surfaces and fatgraphs [arXiv:2307.02706]

Related entries

• supergeometry

• 10d super Yang-Mills theory, IKKT matrix model

category: people