 0098 Lieb E.H., Siedentop H.
 Renormalization of the Regularized Relativistic ElectronPositron Field
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Mar 2, 00

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