Indefinite Metric in State Space
In his Bakerian lecture in 1941 Dirac has suggested that in a relativistic quantum theory, use should be made of a state space with indefinite metric.1 This was a rather revolutionary suggestion, since in unrelativistic quantum theory the state space could always be interpreted as a Hilbert space with positive metric, and the whole probabilistic interpretation of the formalism of quantum theory rested upon this assumption. Dirac’s idea has been developed in the course of years in a great number of papers by many physicists, and it cannot be the intention of the present paper to give a more or less complete historical account of this development. Only its essential steps shall be briefly described and analysed, in order to arrive at conclusions about the significance of Dirac’s suggestion in the present relativistic theory of elementary particles. A few years ago a rather comprehensive survey of this whole field was given in a book by Nagy,2 which also quotes a large part of the related literature.
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