Ghost States in the Lee Model: Renormalization, Indefinite Metrics, and the Limits of Probabilistic Quantum Theory

Hans-Peter Duerr

Renato Ascoli, Ettore Minardi

Rolf Hüper

A special field theoretical model is constructed to study the problem of probability interpretation of a quantum theory with indefinite metric. The model is based on the HEISENBERG dipole-ghost version of the LEE model, but with an additional V Θ-interaction. This interaction yields bound states in the sector N+2 Θ. One gets a situation similar to a case studied by PAULI and KÄLLÉN. It seems that the arising difficulty can be solved only by means of a boundary condition suggested by BOGOLIUBOV. However, such a condition excludes the possibility of interpreting our bound states as “physically realizable” states.

Ali Mostafazadeh

Using the Pais-Uhlenbeck oscillator as a toy model, we outline a consistent alternative to the indefinite-metric quantization scheme that does not violate unitarity. We describe the basic mathematical structure of this method by giving an explicit construction of the Hilbert space of state vectors and the corresponding creation and annihilation operators. The latter satisfy the usual bosonic commutation relation and differ from those of the indefinite-metric theories by a sign in the definition of the creation operator. This change of sign achieves a definitization of the indefinite metric that gives life to the ghost states without changing their contribution to the energy spectrum.

Luigi Accardi, Igor Vasil'evich Volovich, Yun Gang Lu

R. Huper