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.

Selected writings

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

On noncommutative tori:

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

and specifically in relation to T-duality:

On partition functions

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

Introducing the AKSZ sigma-model:

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 (kl|q)(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 (kl|q)(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):

On D=10 super Yang-Mills theory:

On supersymmetry and equivariant localization:

On BV-formalism

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 22D 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,

  • 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:

On quantum mechanics and quantum field theory:

On super Riemann surfaces and fat graphs:

category: people

Last revised on July 7, 2023 at 08:18:09. See the history of this page for a list of all contributions to it.