  Using the quadrature bases that incorporate the spatiotemporal degrees of
freedom, we develop a Wigner functional theory for quantum optics, as an
extension of the Moyal formalism. Since the spatiotemporal quadrature bases
span the complete Hilbert space of all quantum optical states, it does not
require factorization as a tensor product of discrete Hilbert spaces. The
Wigner functions associated with such a space become functionals and operations
are expressed by functional integrals -- the functional version of the star
product. The resulting formalism enables tractable calculations for scenarios
where both spatiotemporal degrees of freedom and particle-number degrees of
freedom are relevant. To demonstrate the approach, we compute examples of
Wigner functionals for a few well-known states and operators.
