Wadim Genrichowitsch Knischnik

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Vadim Genrichovich Knischnik(Russian Вадим Генрихович Книжник, English transliteration Vadim Genrikhovich Knizhnik; born 20 February 1962 in Kiev; † 25 December 1987 in Moscow) was a Russian theoretical physicist.

Knischnik won the USSR Physics Olympiad twice as a high school student, studied at the Moscow Institute of Physics and Technology from 1978 to 1984, and received his PhD (Russian doctoral degree) from the Landau Institute of Theoretical Physics under Alexander Polyakov (Polyakov). In 1986 he joined the Landau Institute, but was also at the ITEP. He placed his first publication while still a student with his professor Alexander Fedorovich Andreev. At the Landau Institute, he was mainly involved in quantum field theory and specifically string theory and quantum gravity.[1] His career as a promising mathematical physicist in the field of string theory was cut short by his early death at the age of only 25.

Knischnik studied loop diagrams of the perturbation series in string theory, using methods of modern algebraic geometry.[2] After him and Alexander Zamolodchikov are named the KZ equations[3] are named after him and Alexander Zamolodchikov, complex partial differential equations of first order, which are obeyed by the correlation functions of conformal field theories to affine Lie algebras.


  • Lars Brink, Daniel Friedan and Polyakov (editors): Physics and Mathematics of Strings. World Scientific, 1990 (Knizhnik Memorial Volume)


  1. Knizhnik, Polyakov and Zamolodchikov: Fractal structure of 2 dimensional quantum gravity. In: Modern Physics Letters A. Vol. 3, 1988, p. 819
  2. Alexander Belavin and Knizhnik: Complex geometry and the theory of quantum strings. In: Soviet Physics JETP. Vol. 64, 1986, pp. 214-228; Belavin and Knizhnik: Algebraic geometry and the geometry of quantum strings. In: Physics Letters B. Vol. 168, 1986, p. 201; Knizhnik: Multiloop Amplitudes in the Theory of Quantum Strings and complex geometry. In: Soviet Physics Uspekhi. Vol. 32, 1989, p. 945
  3. Current Algebra and Wess-Zumino Model in Two-Dimensions. In: Nuclear Physics B. Vol. 247, 1984, pp. 83-103