But we primarily know him as an important quantum physicist. In 1926, he independently derived and generalized (to the case of magnetic fields and velocity-dependent forces) the Klein-Gordon equation, also referred to as the Klein-Fock-Gordon equation.
Because he understood that the harmonic oscillators played a crucial role in quantum field theory, he decided to invent a catchy name for the Hilbert space of a multi-dimensional harmonic oscillator that represents creation and annihilation of particles. Today, we call it the Fock space. ;-) The eigenstates of the number operator are referred to as Fock states.
In 1930, he developed the Hartree-Fock approximation and a related quantity, the Fock matrix, is also named after him.
Einstein, Lenin, Stalin
But what I want to talk about is the relationship between communism and general relativity. Throughout his life, Fock was a loyal Soviet physicist. But it doesn't mean that he always agreed with the communist majority or that he was co-operating on the communist crimes. In fact, the Marxist philosophers used to dislike general relativity while he was the main proponent of GR among his Soviet contemporaries.
For most Marxists, it wasn't quite a Jewish pseudoscience but it looked too abstract for their small working-class brains, too relative and free for their hard-line totalitarian approach to life and freedom, and it was incompatible with various Marxist or Soviet expectations and interpretations, for example the expected infinite extent of both space and time. They also disliked that it was again possible to describe physical phenomena in non-inertial frames (such as the geocentric picture).
These intellectually limited communists were criticizing general relativity for pretty much the same "reasons" as stupid communists in 2007, such as Peter Woit, criticize string theory. I don't want to talk about the incoherent bunk because it made no sense just like it makes no sense today. Read e.g. Gorelik's essay if you want to know a little bit more. What is important is that the dumb yet powerful official Soviet ideologues were imposing certain politically correct restrictions what Soviet scientists could have been doing and believing and general relativity was already outside the box.
However, Fock was ready to paint general relativity as a materialist theory and he managed to get away with it. He was in no way a dissident but he was an example of the people from the "gray zone" who could sometimes do some "moderately courageous" acts. Fock was an honest, dignified, fearless and, strange as it may seem, law-abiding person. Nowadays, Marxists view general relativity as a part of their "scientific" world view. For example, a Marxist page says that
In Einstein’s “general” theory of relativity, the mass of the sun warps the space around the sun. The greater the sun’s mass, the greater the warping effect. A body moving with an initial speed in the neighborhood of the sun will move away from the sun and not be bound to it. But if the initial speed is decreased, a point is reached at which the gravitational pull of the sun will capture the object and it will go into a stable orbit around the sun. Clearly, this qualitative change (the capture of the object into a stable orbit) is brought about by the succession of quantitative changes in the initial speed of the object, which is part of the dialectical process.As you can see, not only general relativity but also perturbation theory are small parts of the Marxist philosophy. The Marxist comments about relativity (and about the general transmutation of quantitative changes into qualitative ones) are completely silly and meaningless but what is important is that this crap helps them to be compatible with a correct theory of physics which is a good thing.
In their relationship towards general relativity and cosmology, Marxists remained obnoxious bigots, see e.g. this 1982 essay by Theckedath, and they have still some problems with the Big Bang and the possible finiteness of the Universe, but they already accept equations of GR, at least in some contexts, and this progress is partially due to the research as well as philosophical interpretations of science by people such as Vladimir Fock.
Both communism and Nazism were trying to influence natural sciences but I would say that the actual impact was much weaker than the impact of environmentalism on climate science or the impact of feminism on biology. The environmentalists are eager to suppress any research of the actual natural mechanisms driving the climate while feminism and other egalitarian ideologies are eager to suppress the research of all parts of biology that unmasks differences between various groups of people. Nazi and communist leaders of science were biased but I am afraid that they were not *that* biased.
And that's the memo.