nLab Albert Schwarz

Albert 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.

• German Wikipedia, Albert S. Schwarz

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

Selected writings

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

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:

• monograph: Quantum field theory and topology, Grundlehren der Math. Wissen. 307, Springer 1993. (translated from Russian original Kvantovaja teorija polja i topologija, Nauka, Moscow, 1989. 400 pp.)

• 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