Vacuum polarization

Vacuum polarization

In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background 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 (photon). Vacuum polarization was observed experimentally in 1997 using the TRISTAN particle accelerator in Japan. [cite journal
last=Levine | first=I. | coauthors=TOPAZ Collaboration
title=Measurement of the Electromagnetic Coupling at Large Momentum Transfer
journal=Physical Review Letters | year=1997
volume=78 | pages=424–427


According to quantum field theory, the ground state of a theory with interacting particles is not simply empty space. Rather, it contains short-lived "virtual" particle-antiparticle pairs which are created out of the vacuum and then annihilate each other.

Some of these particle-antiparticle pairs are 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 if the vacuum were 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:


Vacuum polarization tensor

The vacuum polarization is quantified by the vacuum polarization tensor Πμν(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 Πμν(p) = (p2 gμν - pμpν) Π(p^2) and the subscript 2 denotes the leading order-e2 correction. The tensor structure of Πμν(p) is fixed by the Ward identity.

See also

* Renormalization



* 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.

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