109 FOCK 



Fock worked out a theoretical approach to the wave equation of 

 quantum mechanics for a charged particle in a magnetic field, 

 proving for the first time its "gauge -invariant" properties. As 

 a consequence of the above investigation Fock arrived at the 

 scalar relativistic wave equation for a particle with no spin in 

 an electromagnetic field, independently of similar work by 

 the Swedish physicist O. Klein. This equation is often referred 

 to as the Klein- Fock equation. In 1930 Fock derived from a 

 variational principle the equations of the self- consistent field 

 in the quantum theory of the atom, taking due account of the 

 symmetry properties of the wave function; he developed an ap- 

 proximation method for determining the energy states and 

 transition probabilities of polyelectronic atoms. The method is 

 also used in the theory of molecular structure and in the theory 

 of solids. Fock's most important contributions to the field 

 theory are investigations in second quantization and quantum 

 electrodynamics. In 1932 and 1934 Fock developed a method 

 permitting a quantum description of systems with a variable 

 number of Bose particles (e.g. photons); he uses a functional, 

 dependent on an infinite set of wave functions in spaces of in- 

 creasing number of dimensions (Fock space) and on an auxiliary 

 function (the field variable). In 1939 Fock solved Einstein's 

 gravitational equations for an "insular" distribution of masses 

 (like the Solar system), proving that gravitation equations also ■ 

 include equations of motion. In his monograph "The theory of 

 space, time and gravitation" (1955) Fock interprets Einstein's 

 gravitation theory from his own point of view, drawing a sharp 

 distinction between the physical principle of relativity and the 

 mere co-variance of differential equations; he also insists on 

 the importance of the idea of unity between metric and gravi- 

 tation, as opposed to the idea of relativity of motion, which is of 

 limited application only (according to Fock, a general principle 

 of relativity does not exist). Fock's other scientific achieve- 

 ments are in the integral equation_s, the various applications of 

 conformal representation, the theory of the puncture of di- 

 electrics, the methods based on electricity to detect mineral 

 resources, the theory of core sampling by electrical means, 

 and the theory of diffraction of radio-waves. He also published 

 a number of papers on the interpretation of quantum mechanics. 

 Bibliography: 



The problem of many electrons in quantum mechanics and 

 atomic structure. The 30th Anniversary of the October 

 Revolution, Part I. Mo scow -Leningrad: 1947. 



