  We study the effect of linear transformations on quantum fields with
applications to vertex operator presentations of symmetric functions.
Properties of linearly transformed quantum fields and corresponding
transformations of Hall-Littlewood polynomials are described, including
preservation of commutation relations, stability, explicit combinatorial
formulas and generating functions. We prove that specializations of linearly
transformed Hall-Littlewood polynomials describe all polynomial tau functions
of the KP and the BKP hierarchy. Examples of linear transformations are related
to multiparameter symmetric functions, Grothendieck polynomials, deformations
by cyclotomic polynomials, and some other variations of Schur symmetric
functions that exist in the literature.
