2016/03/31 by Giovanni Collini, Collini, Giovanni
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1603.09626
openalex publication_date 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℏ, which is treated as a deformation parameter. In the limit as ℏ goes to zero, the star product commutator goes to ℏ 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.