Albert Schwarz

From Wikipedia, the free encyclopedia
Jump to: navigation, search
For the Austrian-born American inventor, see Albert Schwarz (inventor).

Albert S. Schwarz[1] (Russian: А. С. Шварц; born June 24, 1934 in Kazan, Soviet Union) is a mathematician and a theoretical physicist educated in Soviet Union and now a Professor at the University of California-Davis. He is one of the pioneers of Morse theory and brought up the first example of a topological quantum field theory. Schwarz worked on some examples in noncommutative geometry. He is the "S" in the famous AKSZ model (named after Mikhail Alexandrov, Maxim Kontsevich, Schwarz, and Oleg Zaboronsky).

In 1990, Schwarz was an invited speaker of the International Congress of Mathematicians in Kyoto.


  • Topology for physicists, Springer 1996
  • 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.)
  • A. S. Švarc, Математические основы квантовой теории поля, (Mathematical aspects of quantum field theory), Atomizdat, Moscow, 1975. 368 pp.

Papers (selection)[edit]

  • Albert Schwarz, Oleg Zaboronsky, Supersymmetry and localization, Comm. Math. Phys. 183, 2 (1997), 463-476
  • M. Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Modern Phys. A 12(7):1405–1429, 1997
  • V. Kac, A. Schwarz, Geometric interpretation of the partition function of 2D gravity, Phys. Lett. B 257 (1991), no. 3-4, 329–334
  • 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
  • V. N. Romanov, A. S. Švarc, Anomalies and elliptic operators, (Russian) Teoret. Mat. Fiz. 41 (1979), no. 2, 190–204
  • S. N. Dolgikh, A. A. Rosly, A. S. Schwarz, Supermoduli spaces, Comm. Math. Phys. 135 (1990), no. 1, 91–100

See also[edit]


  1. ^ Credited as Schwartz in A. A. Belavin et al (1975).


  • Biography
  • Шварц Альберт Соломонович // Воронежская энциклопедия : в 2 т. / Гл. ред. М. Д. Карпачёв. — Воронеж : Центр духовного возрождения Чернозёмного края, 2008. — Т. 2 : Н — Я. — 524 с. : ил., карты.