Fock Space

Fock spaces have interpretations in physics they have been built in order to represent the state space for a system containing an indenite and variable number of identical particles an electron gas photons etc. They are also of great use in quantum eld theory for they provide the setup for the so called second quantization procedure. The fock space is an 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 h.

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We briefly describe how this emergence occurs before proceeding to raise some problems for the naive fock space story.

Fock space. In quantum mechanics a fock state or number state is a quantum state that is an element of a fock space with a well defined number of particles or quanta. These states are named after the soviet physicist vladimir fock. The fock space story is not completely abandoned within the algebraic approach to qft. Fock states play an important role in the second quantization formulation of quantum mechanics.

In fact when conditions are good fock space emerges as the gns hilbert space for some privileged vacuum state of the algebra of observables. Fock spaces were first introduced by v a. Fok in this simplest case. It is named after v.

In the case when the sequences f consist of symmetric functions one speaks of a symmetric or boson fock space and in the case of sequences of anti symmetric functions the fock space is called anti symmetric or fermion. Fock who first introduced it in his 1932 paper konfigurationsraum und zweite quantelung.

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