Untersuchungen Über quantentheorien mit indefiniter metrik

Abstract

The conditions are examined under which a quantum theory with indefinite metric is equivalent to one with difinite metric. The answer to this question depends on general properties of the physical states belonging to that theory. We call a physical state proper, if there exists at least one set of measurements the result of which individuates it completely; otherwise the physical state is called improper. It is necessary and sufficient for the existence of a physically equivalent quantum theory with definite metric, that there be proper physical states only. This result contains the theorem of Ascoli and Minardi 1). There is no form with definite metric of a quantum theory having some improper states among its physical states. In such a theory, one finds, besides an effect already described in ref. 7) that transition probability is not always symmetric.