arXiv 1208.04782012-08-02quant-phastro-ph.COgr-qchep-th

强场中Schwinger级数的性质和对的产生

Properties of the Schwinger series and pair creation in strong fields

B. B. Levchenko

备注：: 4 pages, 2 figures; Based on a report presented at the conference "Lomonosov Readings", MSU, Moscow, Russia, 14 Nov 2011

摘要：

在静态空间均匀电场E中，一对费米子和玻色子的产生几率在Schwinger公式中用无穷级数表示。一般认为，在弱场中，对几率的主要贡献是由级数的第一项给出的，然而显然没有人分析过余项的大小。我们研究的Schwinger级数的数学结构，通过使用在过去的几十年中开发的方法，并证明了给定的系列允许一个精确的总和和剩余增长的贡献迅速与场强。一般来说，只有在强度E >= E_cr的场中，才能从真空中有效地产生粒子对。然而，直接计算表明，产生e+e-对的Schwinger公式仅在场强E < 0.0291*E_cr时才成立。在更高的磁场下，在单位时空体积内产生电子对的几率超过1。在这方面，我们改进了对产生几率的公式，数值计算发现，在E_cr为2.95%的场中，对产生几率几乎为100%。

英文摘要：

Probabilities of a pair of fermions and bosons creation in a static and spatially uniform electric field E are represented in the Schwinger formulas by infinite series. It is believed that in weak fields the main contribution to the probability is given by the first term of series, however the size of the remainder apparently was analyzed by nobody. We study the mathematical structure of the Schwinger series by using methods developed during last decades and prove that the given series allows an exact summation and the contribution of remainder growths rapidly with the field strength. As a rule, it is argued that the pair of particles begin to be produced efficiently from the vacuum only in the fields of strength E >= E_cr. However, the direct calculation shows that the Schwinger formula for creation of e+e- pairs is valid only at the field intensities of E < 0.0291*E_cr. At higher fields, the probability of pair production in an unit space-time volume exceeds unity. In this regard, we refine the formula for the probability of pair creation and numerically find that in the field of strength 2.95% of E_cr the pair production probability is almost 100%.

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