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Asymptotic fields of the lee model

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DOI: 10.1063/1.1664971
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The field equations for the Lee model are solved by constructing eigenfields from the most general possible combination of bare fermion and boson operators. These solutions are found to require an infinite number of boson terms, the coefficients of which obey the integral equations of scattering theory. It is discovered that the algebra of the Lee‐model fermion eigenfields is not that of free particle operators. The anticommutator of the ith fermion eigenfield A i + has the form {A i , A i + } + =1−Σ j≠i A j + A j , where the sum is over all other fermion eigenfields. An algebra of this type is not peculiar to the Lee model. It will hold for all fields which obey a general Pauli exclusion principle and which are orthogonal to one another. The explanation for this algebra lies in the fact that these eigenfields represent operators which create states and not particles. Several other models exhibiting this same behavior (including the harmonic oscillator) are presented; for these models boson fields may also be constructed which have the above algebra. The asymptotic convergence of these eigenfields is not examined. However, it is found that all such Lee‐model fermion fields, including those constructed by the Yang‐Feldman method, must satisfy the above algebra and do not enjoy a free‐fermion canonical algebra.


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