For the canonical commutation relations in infinite dimensions, we offer an explicit direct construction of Weyl representations generated from the Fock representation by polynomial transformations of arbitrary degree, solving a problem posed by Proksch, Reents and Summers. Our solution employs new approaches to Hilbert–Schmidt polynomials and their Wick ordering.
Cite this article
Paul Lee Robinson, Polynomial Weyl Representations. Publ. Res. Inst. Math. Sci. 35 (1999), no. 2, pp. 195–222DOI 10.2977/PRIMS/1195143949