The polynomial relationship between elementary symmetric functions (Cauchy enumeration formula) is formulated via a ``raising operator" and Fock space construction. A simple graphical proof of this relation is proposed. The new operator extends the Heisenberg algebra so that the number operator becomes a Lie product. This study is motivated by natural appearance of these polynomials in the theory of invariants for Lax equations and in classical and topological field theories.

A simple and systematic method for the calculation of group-theoretic weights associated with Feynman diagrams in non-Abelian gauge theories is presented. Both classical and exceptional groups are… Expand