  Considering a fluctuating scalar field on momentum space, some relativistic
statistical field theories are constructed. A Hilbert space of observables is
then constructed from functionals of the fluctuating scalar field with an inner
product defined in terms of expectation values of the functionals. A bosonic
Fock space is then constructed from the Hilbert space and creation and
annihilation operators that act on the Fock space are defined. The creation and
annihilation operators are used to define field operators. These field
operators have some interesting quantum-like properties. For example, the field
operators do not commute in general and, in the particular case of the free
field theory, can be shown to satisfy the microcausality condition.
