Vacuum polarization
The vacuum polarization is a quantum electrodynamic phenomenon, which is closely related to what in quantum field theories commonly known as vacuum fluctuation is called. By creating and destroying virtual particles , the vacuum becomes a non-linearly polarizable electromagnetic medium . Although the vacuum polarization can only be observed indirectly as a small correction in experiments , these confirm the theoretical predictions with sometimes high accuracy. The electrical potential modified by the vacuum polarization is called Uehling potential .
Basics
As in other quantum field theories with interaction, the vacuum is also defined in quantum electrodynamics as the state with the lowest possible energy. In this state, however, the particle number operator has no fixed value, which expresses the fact that the vacuum cannot be regarded as empty. Formally this results because the particle number operator does not commute with the Hamilton operator , which describes the energy of the vacuum state. Although there are no real, directly observable particles in a vacuum, it still has properties that can be explained by the short-term, not directly observable presence of particles. With such descriptions, however, it must be made clear that they are only attempts to illustrate formal theoretical facts, whereby the quantum fields of the particles and the physical measurands formed from them are subject to Heisenberg's uncertainty principle as operators . H. as a rule, cannot form sharply defined expected values.
Feynman diagrams
Feynman diagrams are used in quantum electrodynamics for the clear presentation of complex formulas for the perturbation-theoretical calculation of physical measured quantities. In the lowest order, the vacuum polarization is described by a (virtual) photon , which generates a (virtual) electron - positron pair, which immediately annihilates again to form a (virtual) photon.
If one looks at the diagram in the context of the scattering of two charged particles against one another, e.g. B. of an electron in the electromagnetic field of an atomic nucleus , the electron sees with a weak deflection, i. H. With a small momentum transfer, a smaller electrical charge of the atomic nucleus, shielded by the vacuum polarization, than with a strong deflection, i.e. H. large momentum transfer, whereby it comes much closer to the core and is therefore much less affected by the shielding. However, coming from the classical situation, it is precisely the shielded charge at a large distance that is measured as the classical charge of the atomic nucleus. Therefore, the increase in the interaction at smaller distances is described by an effective increase in the coupling constants with the momentum transfer. Formally, the same diagram is also a contribution to the self-energy of the photon. But it disappears for real photons, which is an expression for the fact that photons are massless.
Virtual electron-positron pairs give the vacuum properties that a non-linearly polarizable medium would have in classical electrodynamics . This becomes particularly clear in the next higher non-zero order of perturbation theory, where the Feynman diagram for the vacuum polarization shows four photons at four corners of a closed electron-positron loop. For example, this diagram predicts the photon-photon scattering , i.e. a process in which two incoming electromagnetic waves are scattered against each other. Such a process is impossible in (linear) classical electrodynamics, where two electromagnetic waves simply add up and therefore penetrate without any interaction. However, the probability for the process is so small that it has not yet been proven. However, there is very good evidence of photon-photon scattering in the data from the ATLAS experiment at CERN .
The same applies to photon splitting, in which an incoming photon is split into two outgoing ones, while the fourth photon in the diagram as a virtual photon mediates the interaction with an external electromagnetic field, e.g. B. again the electromagnetic field of an atomic nucleus. Only the Delbrück scattering , in which two virtual photons mediate the interaction with the electromagnetic field of an atomic nucleus, could actually be measured so far in accordance with the theory.
Experimental evidence
Measurable contributions to the Lamb shift and to particle scattering experiments are regarded as good experimental evidence of vacuum polarization . The contributions of the vacuum polarization to the theoretical value of the anomalous magnetic moment of the electron , the precision measurement of which is compatible with the theory, are particularly good confirmation . The interpretation of the Casimir effect as evidence of vacuum polarization is controversial.
In muonic hydrogen , the vacuum polarization is the dominant contribution to the Lamb shift and has a greater influence than the fine structure .
literature
- Claude Itzykson, Jean-Bernard Zuber: Quantum Field Theory . McGraw-Hill, New York, 1980, ISBN 0-07-032071-3
Individual evidence
- ↑ A more detailed illustration can be found in Chapter 5 of: Stephen Hawking , Leonard Mlodinow : The great design , Rowohlt, Reinbek near Hamburg, 2010, ISBN 978-3-498-02991-3 .
- ↑ A very detailed calculation of this fact can be found in Chapter 7-1-1 by: Claude Itzykson, Jean-Bernard Zuber: Quantum Field Theory , McGraw-Hill, New York, 1980, ISBN 0-07-032071-3 .
- ↑ Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC , The ATLAS Collaboration, https://arxiv.org/pdf/1702.01625.pdf
- ^ I. Levine, TOPAZ Collaboration: Measurement of the Electromagnetic Coupling at Large Momentum Transfer . In: Physical Review Letters . 78, 1997, pp. 424-427. doi : 10.1103 / PhysRevLett.78.424 .
- ^ RL Jaffe: The Casimir Effect and the Quantum Vacuum . In: Physical Review D , Volume 72, 2005 ( web link from Cornell University Library )
- ^ R. Pohl: The size of the proton . In: Nature . 466, 2010, pp. 213-216. doi : 10.1038 / nature09250 .