• Corpus ID: 220936064

Traces, symmetric functions, and a raising operator

  title={Traces, symmetric functions, and a raising operator},
  author={Jerzy Kocik},
  journal={arXiv: Mathematical Physics},
  • Jerzy Kocik
  • Published 1 August 2020
  • Mathematics
  • arXiv: Mathematical Physics
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. 

Figures from this paper


Group theory for Feynman diagrams in non-Abelian gauge 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
Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid
For the study of singular points of dynamical systems it is natural to employ the theory of singularities of mappings (see [1], [2]).