1. It is capable of vacuum polarization . 2. To lowest order \ alpha, virtual pair production generates a vacuum polarization and magnetization given by: 3. The pointlike electron would have a diverging electromagnetic field, which should create a strong vacuum polarization . 4. They also introduced the Euler Heisenberg Lagrangian that laid the basis for the quantitative treatment of vacuum polarization . 5. PVLAS is searching for vacuum polarization of laser beams crossing magnetic fields to detect effects from axion dark matter. 6. Examples include extremely strong fields ( see Euler Heisenberg Lagrangian ) and extremely short distances ( see vacuum polarization ). 7. Thus the vacuum polarization depends on the momentum transfer, or in other words, the dielectric constant is scale dependent. 8. Where \ Pi ^ { \ prime } denotes the derivative of the vacuum polarization function with respect to q 2. 9. In experimental physics, he has worked on a precision measurement of vacuum polarization in muonic atoms to test quantum electrodynamics. 10. This reorientation of the short-lived particle-antiparticle pairs is referred to as "'vacuum polarization " '.