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).After developments in radar equipment for World War II resulted in higher accuracy for measuring the energy levels of the hydrogen atom, Isidor Rabi made measurements of the Lamb shift and the anomalous magnetic dipole moment of the electron.These effects corresponded to the deviation from the value −2 for the spectroscopic electron g-factor that are predicted by the Dirac equation.Later, Hans Bethe[1] theoretically calculated those shifts in the hydrogen energy levels due to vacuum polarization on his return train ride from the Shelter Island Conference to Cornell.Vacuum polarization, referred to below as the one loop contribution, occurs with leptons (electron–positron pairs) or quarks.The former (leptons) was first observed in 1940s but also more recently observed in 1997 using the TRISTAN particle accelerator in Japan,[2] the latter (quarks) was observed along with multiple quark–gluon loop contributions from the early 1970s to mid-1990s using the VEPP-2M particle accelerator at the Budker Institute of Nuclear Physics in Siberia, Russia and many other accelerator laboratories worldwide.[3] Vacuum polarization was first discussed in papers by Paul Dirac[4] and Werner Heisenberg[5] in 1934.Effects of vacuum polarization were calculated to first order in the coupling constant by Robert Serber[6] and Edwin Albrecht Uehling[7] in 1935.[8] According to quantum field theory, the vacuum between interacting particles is not simply empty space.Rather, it contains short-lived virtual particle–antiparticle pairs (leptons or quarks and gluons).These short-lived pairs are called vacuum bubbles.[9][nb 1] Virtual particle–antiparticle pairs can also occur as a photon propagates.The one-loop contribution of a fermion–antifermion pair to the vacuum polarization is represented by the following diagram: These particle–antiparticle pairs carry various kinds of charges, such as color charge if they are subject to quantum chromodynamics such as quarks or gluons, or the more familiar electromagnetic charge if they are electrically charged leptons or quarks, the most familiar charged lepton being the electron and since it is the lightest in mass, the most numerous due to the energy–time uncertainty principle as mentioned above; e.g., virtual electron–positron pairs.Such charged pairs act as an electric dipole.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.Extremely strong electric and magnetic fields cause an excitation of electron–positron pairs.A point charge must be modified at extremely small distances less than the reduced Compton wavelength, the QED result for the electrostatic potential of a point charge is:[11]This can be understood as a screening of a point charge by a medium with a dielectric permittivity, which is why the term vacuum polarization is used.The effects of vacuum polarization become significant when the external field approaches the Schwinger limit, which is:The QED result for slowly varying fields can be written in non-linear relations for the vacuum., virtual pair production generates a vacuum polarization and magnetization given by: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.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 havewhere Πμν(p) = (p2 gμν − pμpν) Π(p2) and the subscript 2 denotes the leading order-e2 correction.The tensor structure of Πμν(p) is fixed by the Ward identity.Vacuum polarization affecting spin interactions has also been reported based on experimental data and also treated theoretically in quantum chromodynamics, as for example in considering the hadron spin structure.