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The necessary extension of the quantum mechanical Hilbert space to a state space with indefinite metric in a local description of quantum electrodynamics, the Yang-Mills theory and a linearized gravitation theory is illustrated. As one of the essential physical consequences of such an extension we emphasize the fact that the interaction cannot be completely represented by the virtual exchange of particles but always does contain non-particle-like “genuine” parts of nonlocal character. In analogy to these cases the indefinite metric in Heisenberg's Lee model and in subcanonical quantum field theories, like Heisenberg's nonlinear spinor theory, is discussed. The physical consequences resulting from a unitarization of these theories with regard to the effective interaction and its causal character are pointed out.

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Über die Rolle einer indefiniten Zustandsmatrix in der Quantenfeldtheorie / About the Role of an Indefinite Metric in the State Space of Quantum Field Theory