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arXiv 1402.0450hep-th
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在路径积分方案中用显式函数限制具有量子涨落的经典杨-米尔斯场的例子

Example of an explicit function for confining classical Yang-Mills fields with quantum fluctuations in the path integral scheme

Kimichika Fukushima, Hikaru Sato

摘要:

本文给出了一种将经典Yang-Mills矢量势和量子涨落限制在经典场周围的显式函数形式。经典矢量势由一个定域函数和一个非定域函数组成,满足经典的杨-米尔斯方程。约束定域函数对威尔逊圈有贡献,而非定域函数对该环无贡献。重费米子和反费米子之间的限制线性势是由于(1)李代数和(2)在时间方向上沿威尔逊圈的粒子和反粒子位置处符号相反的限制定域函数的形式。一些经典的限制部分的矢量势也改变了符号反转的坐标轴垂直于轴连接两个粒子。将矢量势的定域部分压缩在两粒子的连接轴上,导出了约束线性势的弦张力。量子涨落是用实时空中局部基函数的场表达式来表示的。量子路径积分给出了两个粒子之间的库仑势和经典场的线性势。

英文摘要:

This article reports an explicit function form for confining classical Yang-Mills vector potentials and quantum fluctuations around the classical field. The classical vector potential, which is composed of a confining localized function and an unlocalized function, satisfies the classical Yang-Mills equation. The confining localized function contributes to the Wilson loop, while the unlocalized function makes no contribution to this loop. The confining linear potential between a heavy fermion and antifermion is due to (1) the Lie algebra and (2) the form of the confining localized function which has opposite signs at the positions of the particle and antiparticle along the Wilson loop in the time direction. Some classical confining parts of vector potentials also change sign on inversion of the coordinates of the axis perpendicular to the axis joining the two particles. The localized parts of the vector potentials are squeezed around the axis connecting the two particles, and the string tension of the confining linear potential is derived. Quantum fluctuations are formulated using a field expression in terms of local basis functions in real spacetime. The quantum path integral gives the Coulomb potential between the two particles in addition to the linear potential due to the classical fields.

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