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The Lee model was introduced in the 1950s as an elementary quantum fieldtheory in which mass, wave function, and charge renormalization could becarried out exactly. In early studies of this model it was found that there isa critical value of g^2, the square of the renormalized coupling constant,above which g_0^2, the square of the unrenormalized coupling constant, isnegative. Thus, for g^2 larger than this critical value, the Hamiltonian of theLee model becomes non-Hermitian. It was also discovered that in thisnon-Hermitian regime a new state appears whose norm is negative. This state iscalled a ghost state. It has always been assumed that in this ghost regime theLee model is an unacceptable quantum theory because unitarity appears to beviolated. However, in this regime while the Hamiltonian is not Hermitian, itdoes possess PT symmetry. It has recently been discovered that a non-HermitianHamiltonian having PT symmetry may define a quantum theory that is unitary. Theproof of unitarity requires the construction of a new time-independent operatorcalled C. In terms of C one can define a new inner product with respect towhich the norms of the states in the Hilbert space are positive. Furthermore,it has been shown that time evolution in such a theory is unitary. In thispaper the C operator for the Lee model in the ghost regime is constructedexactly in the V/N-theta sector. It is then shown that the ghost state has apositive norm and that the Lee model is an acceptable unitary quantum fieldtheory for all values of g^2.Comment: 20 pages, 9 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Ghost busting:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-symmetric interpretation of the Lee model

Ghost busting:PT-symmetric interpretation of the Lee model