A family of examples with quantum constraints

Abstract

In Rep. Math. Phys. 35 (1995), 101, the authors describe a method for constructing directly (i.e. without using explicitly any field operator nor any concrete representation of the C*-algebra) nets of local C*-algebras associated to massless models with arbitrary helicity and that satisfy Haag–Kastler's axioms. In order to specify the sesquilinear and the symplectic form of the CAR- and CCR-algebras, respectively, a certain operator-valued function β(·) is introduced. This function is shown to be very useful in proving the covariance and causality of the net and it also codes the degenerate character of massless models with respect to massive models.

It is the intention of this Letter to point out that the massless bosonic examples with helicity bigger than 0 fit completely into the general theory that Grundling and Hurst used to describe systems with gauge degeneracy.