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arXiv 1402.5641nucl-thhep-ph
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库仑规范和洛伦兹规范中电子-质子散射的场论公式

On the field theoretical formulation of the electron-proton scattering in the Coulomb and Lorentz gauges

A. I. Machavariani

摘要:

基于量子电动力学中的幺正性条件,导出了相对论性三维Lippmann-Schwinger型$ep$散射振幅方程. $ep$散射势$V_{e'N',eN}$由领先的一次性质量壳层光子交换势和非局域多粒子交换势组成。与其他场论方程不同,在么正性条件下和$V_{e'N',eN}$中的质子都在质量壳层上。因此,在这种方法中不需要多变量输入光子核子顶点与质量壳核子。在本公式中,标准的领先单光子交换势$V_{OPE}$是由电子源和相互作用的电子场之间的正则等时反换位子产生的,而电子场被单核子渐近态夹在中间.这个反交换子是在库仑和洛伦兹规范中计算的,其中只有光子场的横向部分是量子化的。结果表明,库仑规范和洛仑兹规范中的主导单光子交换势n $V_{OPE}$是一致的。精确地再现了由静电(库仑)相互作用产生的次至首阶项的完整集合。

英文摘要:

The relativistic three dimensional (3D) Lippmann-Schwinger-type equations for the $ep$ scattering amplitude is derived based on unitarity condition in the usual quantum electrodynamic (QED). The $ep$ scattering potential $V_{e'N',eN}$ consists of the leading one off mass shell photon exchange part and the nonlocal multi-particle exchange potential. Unlike to the other field-theoretical equations, both protons in the unitarity condition and in $V_{e'N',eN}$ are on mass shell. Therefore in this approach are not required the multi-variable input photon-nucleon vertexes with the off mass shell nucleons. In the present formulation the standard leading one photon exchange potential $V_{OPE}$ is generated by the canonical equal-time anti commutator between the electron source and the interacted electron fields which are sandwiched by the one nucleon asymptotic states. This anticommutator is calculated in the Coulomb and Lorentz gauges, where only the transverse parts of the photon fields are quantized. It is shown, that the leading one photon exchange potentialn$V_{OPE}$ in the Coulomb and Lorentz gauges coincide. The complete set of the next to leading order terms which are generated by the static electric (Coulomb) interaction are exactly reproduced.

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