Abstract
The question on the existence of a physical Hilbert subspace in a field theory with indefinite metric is investigated in an extended Lee model. The interaction Hamiltonian of the original Lee model is generalized to contain an infinite set of terms representing the basic interaction processes, V+nθ↔N+(n+1)θ,n=1, 2, 3, ..., besides the usual trilinear term. The bare field operators are transformed into «clothed» field operators according to the unitary clothing transformations of Greenberg and Schweber, so that the conditions for separating out the «ghost» states are easi y sought. It is found that a physical Hilbert subspace exists in this model provided that the cut-off functions introduced have certain special forms.
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