On the structure of the $C^*$-algebra generated by the field operators

Vladimir Georgescu, Andrei Iftimovici

Published 2019-02-26Version 1

We study the $C^*$-algebra generated by the field operators associated to representations of a symplectic space and the operators affiliated to it. We show that the algebra is graded by the semilattice of all finite dimensional subspaces of the symplectic space and in the finite dimensional case we give an intrinsic description of the components of the grading.