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
The effects of vacuum polarization have been routinely observed experimentally since then as very well-understood background effects. 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]
History
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]
Explanation
According to
Virtual particle–antiparticle pairs can also occur as a photon propagates.[10] In this case, the effect on other processes is measurable. 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
Electric and magnetic fields
Extremely strong electric and magnetic fields cause an excitation of electron–positron pairs. Maxwell's equations are the classical limit of the quantum electrodynamics which cannot be described by any classical theory. A point charge must be modified at extremely small distances less than the reduced Compton wavelength (). To lowest order in the fine-structure constant, , 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. When observed from distances much greater than , the charge is renormalized to the finite value . See also the Uehling potential.
The effects of vacuum polarization become significant when the external field approaches the Schwinger limit, which is:
These effects break the linearity of Maxwell's equations and therefore break the superposition principle. The QED result for slowly varying fields can be written in non-linear relations for the vacuum. To lowest order , virtual pair production generates a vacuum polarization and magnetization given by:
As of 2019,[update] this polarization and magnetization has not been directly measured.
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
Note
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.
See also
- Renormalization
- Virtual particles
- QED vacuum
- QCD vacuum
- Schwinger limit
- Schwinger effect
- Uehling potential
- Vacuum birefringence
Remarks
- ^ They yield a phase factor to the vacuum to vacuum transition amplitude.
Notes
- ^ Bethe 1947
- ^ Levine 1997
- ^ Brown & Worstell 1996, pp. 3237–3249
- ^ Dirac 1934
- ^ Heisenberg 1934
- ^ Serber 1935
- ^ Uehling 1935
- ^ Gell-Mann & Low 1954
- ^ Greiner & Reinhardt 1996, Chapter 8.
- ^ Weinberg 2002, Chapters 10–11
- ^ Berestetskii, Lifshitz & Pitaevskii 1980, Section 114.
References
- Berestetskii, V. B.; ISBN 978-0750633710.
- Wikidata Q21709244.
- Brown, Douglas H.; Worstell, William A (1996). "The Lowest Order Hadronic Contribution to the Muon g − 2 Value with Systematic Error Correlations". Physical Review D. 54 (5) (published 1 September 1996): 3237–3249. Wikidata Q27349045.
- Wikidata Q60895121.
- Wikidata Q21709149.
- ISBN 978-3-540-59179-5.
- Wikidata Q56068099.
- Levine, I.; et al. (TOPAZ Collaboration) (1997). "Measurement of the Electromagnetic Coupling at Large Momentum Transfer". Physical Review Letters. 78 (3) (published January 1997): 424–427. Wikidata Q21698757.
- Wikidata Q60895120.
- Uehling, E. A. (1935). "Polarization Effects in the Positron Theory". Phys. Rev. 48 (1) (published 1 July 1935): 55–63. Wikidata Q60895119.
- ISBN 978-0-521-55001-7.
Further reading
- 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.