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arXiv 0803.4173hep-ph
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磁场作用下QED的动态质量生成:任意场强和耦合常数

Dynamical mass generation in QED with magnetic fields: arbitrary field strength and coupling constant

Eduardo Rojas, Alejandro Ayala, Adnan Bashir, Alfredo Raya

摘要:

通过求解彩虹近似下费米子自能的Schwinger-Dyson方程,研究了在任意强度的磁场存在下,猝灭量子电动力学中基本费米子质量的动态产生.我们采用的Ritus特征函数形式主义,它提供了一个整洁的解决方案的技术问题,总结所有朗道水平。众所周知,对于任意小的电磁耦合α值,磁场会催化费米子质量m的产生。对于强场,还公知m \propto \sqrt eB.我们的方法允许我们跨越参数α和eB的所有区域。我们发现,当α较小时,m \propto \sqrt eB.然而,当α增加到超过临界值α_c时,我们发现m \propto Λ,这是正则化紫外发散所需的截止值。我们的方法使我们能够验证文献中关于eB和α极限情况的结果。我们还指出了我们的工作可能的物理应用的相关性。

英文摘要:

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics, in the presence of magnetic fields of arbitrary strength, by solving the Schwinger-Dyson equation (SDE) for the fermion self-energy in the rainbow approximation. We employ the Ritus eigenfunction formalism which provides a neat solution to the technical problem of summing over all Landau levels. It is well known that magnetic fields catalyze the generation of fermion mass m for arbitrarily small values of electromagnetic coupling α. For intense fields it is also well known that m \propto \sqrt eB. Our approach allows us to span all regimes of parameters αand eB. We find that m \propto \sqrt eB provided αis small. However, when αincreases beyond the critical value α_c which marks the onslaught of dynamical fermion masses in vacuum, we find m \propto Λ, the cut-off required to regularize the ultraviolet divergences. Our method permits us to verify the results available in literature for the limiting cases of eB and α. We also point out the relevance of our work for possible physical applications.

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