Renormalization of the Regularized Relativistic Electron-Positron Field

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.

11 pages, latex2e

Cited by in corpus (9)

• Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation
• Self-consistent solution for the polarized vacuum in a no-photon QED model
• A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics
• Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
• Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
• Renormalization and asymptotic expansion of Dirac's polarized vacuum
• Ground state properties of graphene in Hartree-Fock theory
• Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics
• Existence of Ground State of an Electron in the BDF Approximation