A note on regular states and supplementary conditions (Q1109306)

The author points out that in the presence of linear Hermitian constraints on linear boson theories, any attempt to impose them as eigenvalue conditions on physical states will fail because such states do not exist. Similarly, the use of von Neumann algebras will not be successful if weak continuity is demanded. It is shown that if an abstract C *-algebra is used in order to construct the final physical algebra from a CCR-algebra, then all these difficulties disappear. For the final physical algebra suitable regular states exist, and all evidences of unacceptable discontinuities will be confined to nonphysical elements.