阿贝尔规范场的非动力学势的协变隔离,当反馈时,它可以转化为“限制Yukawa”
Covariant isolation from an Abelian gauge field of its nondynamical potential, which, when fed back, can transform into a "confining Yukawa"
摘要:
对于阿贝尔规范理论,通过对电荷密度的延迟库仑变换,用四维势的时间分量的因果决定来补充洛伦兹条件,从而发展出一种恰当的相对论规范。对于静电荷密度,这种因果洛伦兹规范与库仑规范一致,但允许四矢量势具有由四矢量势的时间分量的时间导数确定的纵向分量。正如在库仑规范中一样,四矢势的两个横分量是它唯一的动力学部分。这个规范中的四维势协变地分离为一个动力学的横向四维势和一个非动力学的类时/纵向四维势,其中每一个都满足洛伦兹条件。事实上,四元守恒流的类似划分表明,每一元守恒流都满足一个具有自己的四元守恒流的洛伦兹条件麦克斯韦方程组。由于这种完全分离,这四个矢量势中的任何一个都可以被修补而不影响它的对应物。由于它满足洛伦兹条件,非动力学四维势乘以一个长度平方倒数的常数本身就是一个守恒的四维流,因此可以反馈到它自己的源电流中,源电流将其时间分量转换为一个扩展的汤川,其中既有指数衰减的分量,也有指数增长的分量。后者可能是夸克-胶子禁闭的机制:在非阿贝尔色规范理论中,汤川混合比应该与颜色有关,这对“多彩的”热夸克-胶子等离子体有明显的影响。
英文摘要:
For Abelian gauge theory a properly relativistic gauge is developed by supplementing the Lorentz condition with causal determination of the time component of the four-vector potential by retarded Coulomb transformation of the charge density. This causal Lorentz gauge agrees with the Coulomb gauge for static charge densities, but allows the four-vector potential to have a longitudinal component that is determined by the time derivative of the four-vector potential's time component. Just as in Coulomb gauge, the two transverse components of the four-vector potential are its sole dynamical part. The four-vector potential in this gauge covariantly separates into a dynamical transverse four-vector potential and a nondynamical timelike/longitudinal four-vector potential, where each of these two satisfies the Lorentz condition. In fact, analogous partition of the conserved four-current shows each to satisfy a Lorentz-condition Maxwell equation system with its own conserved four-current. Because of this complete separation, either of these four-vector potentials can be tinkered with without affecting its counterpart. Since it satisfies the Lorentz condition, the nondynamical four-vector potential times a constant with dimension of inverse length squared is itself a conserved four-current, and so can be fed back into its own source current, which transforms its time component into an extended Yukawa, with both exponentially decaying and exponentially growing components. The latter might be the mechanism of quark-gluon confinement: in non-Abelian color gauge theory the Yukawa mixture ratio ought to be tied to color, with palpable consequences for "colorful" hot quark-gluon plasmas.
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