The
Fock space is an
algebraic system used in
quantum mechanics to describe
quantum states with a variable or unknown number of
particles. It is named after
V. A. Fock.
Technically, the Fock space is the Hilbert space made from the direct sum of tensor products of single-particle Hilbert spaces
where S? is the operator which symmetrizes or antisymmetrizes the space, depending on whether the Hilbert space describes particles obeying bosonic (? = + ) or fermionic (? = - ) statistics respectively. H is the single particle Hilbert space. It describes the quantum states for a single particle, and to describe the quantum states of systems with n particles, or superpositions of such states, one must use a larger Hilbert space, the Fock space, which contains states for unlimited and variable number of particles. Fock states are the natural basis of this space. (See also the Slater determinant.)
It has been observed that free symmetric algebra construction can provide a model of the linear modality[1]. This construction arose independently in quantum physics, where it is considered as a canonical model of quantum field theory. In this context, the construction is known as (bosonic) Fock space. Fock space is used to analyze such quantum phenomena as the annihilation and creation of particles. There is a strong intuitive connection to the principle of renewable resources, which is the philosophical interpretation of the linear modalities.
