Vacuum polarization

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In quantum field theory, vacuum polarization describes a process in which an electromagnetic field produces virtual electron-positron pairs that change the distribution of charges and currents that generated the original electromagnetic field. It is also sometimes referred to as the self energy of the gauge boson.

In quantum physics, if we expand about the Fock vacuum, the true vacuum contains short-lived "virtual" particle-antiparticle pairs which are created in pairs out of the Fock vacuum and then annihilate each other. Some of these particle-antiparticle pairs turn out to be charged; e.g., virtual electron-positron pairs. Such charged pairs act as an electric dipole. In the presence of an electric field, e.g., the electromagnetic field around an electron, these particle-antiparticle pairs reposition themselves, thus partially counteracting the field (a partial screening effect, a dielectric effect). The field therefore will be weaker than would be expected when the vacuum would be completely empty. This reorientation of the short-lived particle-antiparticle pairs is referred to as vacuum polarization.

The one-loop contribution of a fermion-antifermion pair to the vacuum polarization is represented by the following diagram:

The vacuum polarization is quantified by the vacuum polarization tensor Π^μν(p) which describes the dielectric effect as a function of the four-momentum p carried by the photon. Thus the vacuum polarization depends on the momentum transfer, or in other words, the dielectric constant is scale dependent. In particular, for electromagnetism we can write the fine structure constant as an effective momentum-transfer-dependent quantity; to first order in the corrections, we have

$\alpha_{eff}(p^2) = \frac{\alpha}{1 - [\Pi_2(p^2) - \Pi_2(0)]}$

where Π^μν(p) = (p² g^μν - p^μp^ν) Π(p^2) and the subscript 2 denotes the leading order-e² correction. The tensor structure of Π^μν(p) is fixed by the Ward identity.

[edit] See also

Renormalization

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Quantum electrodynamics v • d • e
electron \| positron \| photon self-energy \| vacuum polarization \| vertex function Gupta-Bleuler formalism \| ξ gauge \| Ward identities Compton scattering \| Bhabha scattering \| Moeller scattering anomalous magnetic dipole moment bremsstrahlung \| positronium

[edit] References

For a derivation of the vacuum polarization in QED, see section 7.5 of M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, 1995.