CONSTRUCTION OF VACUUM FOR THE POSITIVE-ENERGY REPRESENTATION AND ITS BOSE COUNTERPART

摘要

In [3] Lundberg constructed a vacuum for the positive energy representation of CAR (cf. [1]) using the GNS-construction as a main tool. In the present paper we produce the same re?presentation using the embedding-in-the-dual technique, as proposed in [8]. The advantage of this way of approach lies in the fact that both the original representation and its Dirac (and Schrodinger) version (cf. [8]) act within a common domain named the master extension. In the master extension we construct two vacuum-representations. Each one can be the positive energy representation using the other representation as reference. Since an almost identical procedure can be used with respect to the representation of CCR given by Wakimoto [9], we show the two procedures simultaneously.