1. QED Correction to Radiation from Magnetors Takahiro Hayashinaka 林中貴宏 (RESCEU, U. Tokyo) Work in prep. with Teruaki Suyama (RESCEU, U. Tokyo)

2. Preview - Magnetic field of Neutron Stars From Nobelprize.org P-P dot diag. Courtesy of Nakano-san, form the data of ATNF Pulsar catalogue

3. Nobody knows !

4. About QED Elementary process of QEDTypical scale (strength) of Electric field Magnetic field

5. Loop effect – diagram

6. Loop effect – Effective photon action Euler-Heisenberg Lagrangian Proper time Vacuum renormalization Charge renormalization Effective action for constant EM field is valid even under the slow varying assumption. Original kinetic term c.f. derivative expansion : J.Math.Phys. 40 (1999) 5406-5439

7. Equation of Motion Variation of the Effective action gives corrected Maxwell eq. External source (current generated by NS) 1-loop correction from fermion

8. Review – Classical Magnetic dipole radiation Solution far away from the source = radiation

9. Equation of Motion Variation of the Effective action gives corrected Maxwell eq. External source (current generated by NS) 1-loop correction from fermion

10. Equation of Motion - perturbation External source (current generated by NS) 1-loop correction from fermion Variation of the Effective action gives corrected Maxwell eq.

11. First order result Mainly contributed from BBB-term e.g. highly localized current right on the equator : (prefactor) = O(0.1) Correction term depends on the geometry (configuration) of NS current

12. Effective photon action (Again) Euler-Heisenberg Lagrangian

13. Strong field limit Using Ramanujan-Sitaramachandrarao’s formula, EH Lagrangian can be integrated and taking Strong |B| limit gives the leading behavior: which express the correction to the kinetic term. There is no correction beyond running of coupling effect, and radiation looks like classical electromagnetism with changed coupling.

14. summary We found the 1-loop QED correction term to the magnetic dipole radiation explicitly. It looks like, but not much larger than O(0.1). When the field strength goes extremely large, there would be NO correction.