  Fedosov has described a geometro-algebraic method to construct in a canonical
way a deformation of the Poisson algebra associated with a finite-dimensional
symplectic manifold ("phase space"). His algorithm gives a non-commutative, but
associative, product (a so-called "star-product") between smooth phase space
functions parameterized by Planck's constant $\hbar$, which is treated as a
deformation parameter. In the limit as $\hbar$ goes to zero, the star product
commutator goes to $\hbar$ times the Poisson bracket, so in this sense his
method provides a quantization of the algebra of classical observables. In this
work, we develop a generalization of Fedosov's method which applies to the
infinite-dimensional symplectic "manifolds" that occur in Lagrangian field
theories. We show that the procedure remains mathematically well-defined, and
we explain the relationship of this method to more standard perturbative
quantization schemes in quantum field theory.
