Gerstein–Greiner–Zeldovich Effect: Induced Charge Density and Vacuum Energy

IF 0.4 Q4 PHYSICS, PARTICLES & FIELDS Physics of Particles and Nuclei Letters Pub Date : 2024-04-09 DOI:10.1134/s1547477124020067

P. A. Grashin, K. A. Sveshnikov

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Abstract

The Gerstein–Greiner–Zeldovich effect—the spontaneous emission of vacuum positrons under conditions of Coulomb supercriticality—has been studied in detail based on the first principles of quantum electrodynamics within the framework of an essentially nonperturbative approach based on a special combination of analytical methods, computer algebra, and numerical calculations. Particular attention is paid to the vacuum energy \({\kern 1pt} {{\mathcal{E}}_{{{\text{VP}}}}}\), considered a function of the parameters of the external Coulomb source: charge \(Z\) and radius \(R\). The specific contribution to \({\kern 1pt} {{\mathcal{E}}_{{{\text{VP}}}}}\) arising due to the direct Coulomb interaction of the vacuum charge densities \({{\varrho }_{{{\text{VP}}}}}(\vec {r})\) has been studied in detail. It is shown that, with correct renormalization, this contribution becomes negative after the first discrete levels descend into the lower continuum. Therefore, it is a purely quantum effect, not observed in classical electrodynamics. The problem of lepton number conservation during spontaneous emission is also discussed.

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格斯坦-格里纳-泽尔多维奇效应：诱导电荷密度和真空能量

摘要根据量子电动力学的第一原理，在一种基于分析方法、计算机代数和数值计算特殊组合的基本非扰动方法框架内，对格斯坦-格里纳-泽尔多维奇效应--库仑超临界条件下真空正电子的自发发射--进行了详细研究。特别关注的是\({\kern 1pt} {{\mathcal{E}}_{{text/{VP}}}}}\) 的真空能，它被认为是外部库仑源参数的函数：电荷\(Z\) 和半径\(R\)。我们详细研究了由于真空电荷密度的直接库仑相互作用而产生的对\({\varrho }_{{text/{VP}}}}}(\vec {r})\)的具体贡献。研究表明，在正确的重正化条件下，当第一个离散级下降到低连续体之后，这个贡献就会变成负值。因此，这是一种纯量子效应，在经典电动力学中观察不到。此外，还讨论了自发发射过程中的轻子数目守恒问题。

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来源期刊

Physics of Particles and Nuclei Letters PHYSICS, PARTICLES & FIELDS-

CiteScore

0.80

自引率

20.00%

发文量

108

期刊介绍： The journal Physics of Particles and Nuclei Letters, brief name Particles and Nuclei Letters, publishes the articles with results of the original theoretical, experimental, scientific-technical, methodological and applied research. Subject matter of articles covers: theoretical physics, elementary particle physics, relativistic nuclear physics, nuclear physics and related problems in other branches of physics, neutron physics, condensed matter physics, physics and engineering at low temperatures, physics and engineering of accelerators, physical experimental instruments and methods, physical computation experiments, applied research in these branches of physics and radiology, ecology and nuclear medicine.