FOCK SPACE

FOCK, V. [VLADIMIR ALEKSANDROVICH FOK].

Konfigurationsraum und Zweite Quantelung.

Berlin, Springer, 1932. 8vo. Bound in contemporary half cloth with gilt lettering, In "Zeitschrift für Physik", Band 75, 1932. Entire volume offered. Two stamps to title page, otherwise fine. Pp. 622-647. [Entire volume: VIII, 850 pp + frontiespiece].

First appearance of Fock's seminal paper in which he introduced his algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space, often referred to as Fock space.
Technically, the Fock space is (the Hilbert space completion of) the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space H.

"Between 1928 and 1934, Fok obtained important results in the quantum field theory. He completed the mathematical method of secondary quantization proposed by Paul A.M. Dirac and developed by Pascual Jordan and Eugene Wigner. It has been shown that this method does not go beyond the traditional framework of quantum mechanics (as Jordan argued) and that the two ways of description are completely equivalent. As early as 1934 Fok suggested describing a system with a variable number of particles (bosons) in the representations of the secondary quantization with the aid of a generating functional ("Fok’s functional").In his papers Fok introduced a number of new notions. such as "the Fok space" (a Hilbert space in the representation of secondary quantization). In papers written with Dirac and Boris Podolsky (1932), Dirac’s results on interaction of charged particles by the exchange of virtual photons were extended. The one-dimensional problem solved by Dirac was generalized to the realistic three-dimensional case: the multitime formalism of Dirac, Podolsky, and Fok was introduced; and quantum electrodynamics was formulated in its modern form." (DSB).

Order-nr.: 49257