Vacuum polarization

The vacuum polarization is a quantum electrodynamic phenomenon, which is closely related with what is commonly referred to in quantum field theories as a vacuum fluctuation. Through creation and annihilation of virtual particles is thereby the vacuum to a nonlinear electromagnetic polarizable medium. Although the vacuum polarization is only indirectly observable as a small correction in experiments, these confirm the theoretical predictions with partly high accuracy.

Basics

As in other quantum field theories with interaction, the vacuum is defined as the state with the lowest possible energy in quantum electrodynamics. However, the particle number has no fixed value, which is expressing the fact that one can not interpret as empty the vacuum in this state. Formally, the results, because the particle number operator does not commute with the Hamiltonian, which describes the energy of the vacuum state. Although no real vacuum, directly observable particles are present, but it has properties that can be explained by a brief, not directly observable presence of particles. However, it must be in such descriptions make it clear that they are only attempts to illustrate formal theoretical facts, wherein the quantum fields of the particles formed therefrom and physical parameters are subject to as operators of heisenberg 's uncertainty relation, ie usually can not form a sharply defined expectation values ​​.

Feynman diagrams

Feynman diagrams used in quantum electrodynamics for the graphic presentation of complicated formulas for the perturbative calculation of physical quantities. In the lowest order vacuum polarization is described by a ( virtual ) photon, which creates a ( virtual ) electron-positron pair, which destroyed immediately to a (virtual) photon.

Looking at the diagram in the context of scattering of two charged particles to each other, eg of an electron in the electromagnetic field of an atomic nucleus, the electron sees in low distraction, ie small momentum transfer, a smaller, shielded by the vacuum polarization electric charge of the nucleus than in strong distraction, ie large momentum transfer, with it comes much closer to the core and is therefore much less affected by the shielding. But Coming from the classical situation is just the shielded charge at a large distance that which is measured as a classical charge of the atomic nucleus. Therefore, to describe the increase of the interaction at smaller intervals by an effective increase of the coupling constant with the momentum transfer. Formally, the same diagram is also a contribution to the self-energy of the photon. But vanishes for real photons, which is an expression of the fact that photons are massless.

Virtual electron-positron pairs give the vacuum properties that aufwiese in classical electrodynamics a nonlinearly polarizable medium. This is particularly clear in the next higher non-vanishing order of perturbation theory, where the Feynman diagram for the vacuum polarization has four photons at four corners of a closed electron-positron loop. By this diagram, the photon-photon scattering is predicted, for example, that is a process in which two incoming electromagnetic waves are dispersed to each other. Such a process is impossible in the (linear) classical electrodynamics, where two electromagnetic waves easily add and therefore penetrate without any interaction. The probability of the process is so small that it has not yet been demonstrated.

The same applies for the photocleavage, wherein an incoming photon is split into two outgoing, while the fourth photon interaction in the diagram provides a virtual photon with an external electromagnetic field, for example again the electromagnetic field of an atomic nucleus. Only the Delbruck scattering, where two virtual photons mediate the interaction with the electromagnetic field of an atomic nucleus, has so far actually measured in accordance with the theory.

Experimental evidence

As good experimental evidence of the vacuum polarization measurable contributions to the Lamb shift and Teilchenstreuexperimenten apply. A particularly good confirmation provide the contributions of vacuum polarization to the theoretical value of the anomalous magnetic moment of the electron, its measurement precision is compatible with the theory. The interpretation of the Casimir effect as proof of the vacuum polarization is controversial.

In muonic hydrogen, the vacuum polarization is the dominant contribution to the Lamb shift and has a greater impact than the fine structure.