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Renormalization of the Regularized Relativistic Electron-Positron Field

Elliott H. Lieb·Heinz Siedentop
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Abstract

We consider the relativistic electron-positron field interacting with itself via the Coulomb potential defined with the physically motivated, positive, density-density quartic interaction. The more usual normal-ordered Hamiltonian differs from the bare Hamiltonian by a quadratic term and, by choosing the normal ordering in a suitable, self-consistent manner, the quadratic term can be seen to be equivalent to a renormalization of the Dirac operator. Formally, this amounts to a Bogolubov-Valatin transformation, but in reality it is non-perturbative, for it leads to an inequivalent, fine-structure dependent representation of the canonical anticommutation relations. This non-perturbative redefinition of the electron/positron states can be interpreted as a mass, wave-function and charge renormalization, among other possibilities, but the main point is that a non-perturbative definition of normal ordering might be a useful starting point for developing a consistent quantum electrodynamics.

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Elliott H. Lieb, Heinz Siedentop. 2000-03-02. Renormalization of the Regularized Relativistic Electron-Positron Field. https://doi.org/10.1007/s002200000265

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