Zeta Function Regularization of Photon Polarization Tensor for a Magnetized Vacuum
| Autor: | Chao, Jingyi, Yu, Lang, Huang, Mei |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Phys. Rev. D 90, 045033 (2014) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.90.045033 |
| Popis: | In this paper, we have developed a systematic technique to regularize double summations of Landau levels and analytically evaluated the photon vacuum polarization at an external magnetic field. The final results are described by Lerch transcendent $\Phi(z,s,v)$ or its $z$-derivation. We have found that the tensor of vacuum polarization is split into not only longitudinal and transverse parts but also another mixture component. We have obtained a complete expression of the magnetized photon vacuum polarization at any kinematic regime and any strength of magnetic field for the first time. In the weak $B$-fields, after canceling out a logarithmic counter term, all three scalar functions are limited to the usual photon polarization tensor without turning on magnetic field. In the strong $B$-fields, the calculations under Lowest Landau Level approximation are only valid at the region $M^2\gg q_{\shortparallel}^2$, but not correct while $q_{\shortparallel}^2\gg M^2$, where, an imaginary part has been missed. It reminds us, a recalculation of the gap equation under a full consideration of all Landau Levels is necessary in the next future. Comment: 7 pages. One severe mistake has been corrected and two references have been updated |
| Databáze: | arXiv |
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