# Fok, Vladimir

## Fok, Vladimir Aleksandrovich

(also V. A. Fock). Born Dec. 10 (22), 1898, in St. Petersburg; died Dec. 27, 1974, in Leningrad. Soviet physicist. Academician of the Academy of Sciences of the USSR (1939; corresponding member, 1932). Hero of Socialist Labor (1968).

After graduating from Petrograd University in 1922, Fok remained there to attend graduate school. From 1919 to 1923 and from 1928 to 1941 he was a research worker at the State Optics Institute, and from 1924 to 1936 at the Leningrad Physicotechnical Institute. At the same time, beginning in 1932, he was a professor at Leningrad University. From 1934 to 1941 and again from 1944 to 1953 he was a research worker at the Institute of Physics of the Academy of Sciences of the USSR. Between 1954 and 1964 he worked at the Institute for Physical Problems of the Academy of Sciences of the USSR.

Fok’s main works dealt with gravitational theory, quantum field theory, the theory of many-electron systems, functional methods in field theory and statistical physics, the propagation of radio waves, diffraction theory, and mathematical physics. His early works were devoted to the mechanics of continuous mediums and theoretical optics. In his work on the computation of illuminance, Fok laid the basis for the vector theory of a light field. The most important result of his studies in mechanics was the solution of the two-dimensional problem in the theory of elasticity by means of Fredholm’s integral equations.

In 1926, Fok generalized the wave equation of quantum mechanics for the case of a magnetic field and was the first to demonstrate the gauge invariance of the equation. He derived, independently of the Swedish physicist O. Klein and the German physicist W. Gordon, the relativistic scalar equation, sometimes called the Klein-Gordon-Fok equation. In 1930 he examined the self-consistent field equation in the quantum theory of a many-electron system with the Pauli principle taken into account and developed an approximate method of describing and calculating the equation (the Hartree-Fok method). His studies of second quantization and quantum electrodynamics yielded important results for quantum field theory. In 1934, Fok developed the method of functionals for the theory of systems having a variable number of particles. Within the framework of the gravitational theory of A. Einstein, he derived approximate equations of motion for a system of bodies.

Fok’s works in mathematics and mathematical physics covered a broad area, including integral equations, the theory of numerical integration, various applications of conformal mapping, the theory of dielectric breakdown, electrical mineral prospecting methods, and the theory of well logging. Fok completed a number of fundamental studies on the theory of radio-wave propagation (State Prize of the USSR, 1946), as well as studies on methodological problems in quantum mechanics and relativity theory.

Fok received the Lenin Prize in 1960. He was awarded four Orders of Lenin, the Order of the Red Banner of Labor, and various medals.

### WORKS

*Nachala kvantovoi mekhanki*, 2nd ed. Moscow, 1976.

*Raboty po kvantovoi teorii polia*. [Leningrad] 1957.

*Teoriia prostranstva, vremeni i tiagoteniia*, 2nd ed. Moscow, 1961.

### REFERENCE

*Vladimir Aleksandrovich Fok*. Moscow, 1956. (

*AN SSSR: Materialy k biobibliografii uchenykh SSSR. Seriia fiziki*, no. 7.)