玻恩能级束缚态
Born Level Bound States
摘要：
微扰QED的$S$ -矩阵中的束缚态极点是由$α$展开的{ \em散度}产生的。当在自由态、\order{α^0} $in$和$out$态周围展开时，微扰修正必然是奇异的，这些态与有限尺寸的原子波函数没有重叠。然而，可测量的量，如结合能，确实具有$α$（和$\logα$）幂的良好展开。规范理论束缚态的“最低阶”概念是理想的，使得高阶修正在$α\to 0$极限中消失。这可能允许确定QCD强子的最低阶项，它包含了诸如禁闭和手征对称性破缺等基本特征，因此可以作为有用的微扰展开的起点。我讨论了一个“Born”（没有循环，在$\hbar$中的最低阶）近似。玻恩能级态被满足经典场方程的规范场束缚。高斯定律为电荷的每个瞬时位置确定不同的场$A^0(\xv)$。胶子场的庞加莱协变边界条件导致$q\bar q$和$qqq$态的限制势。在束缚态处于运动中的标架中，经典规范场是由静止标架场的洛仑兹增强得到的。
英文摘要：
Bound state poles in the $S$-matrix of perturbative QED are generated by the {\em divergence} of the expansion in $α$. The perturbative corrections are necessarily singular when expanding around free, \order{α^0} $in$ and $out$ states that have no overlap with finite-sized atomic wave functions. Nevertheless, measurables such as binding energies do have well-behaved expansions in powers of $α$ (and $\logα$). It is desirable to formulate the concept of "lowest order" for gauge theory bound states such that higher order corrections vanish in the $α\to 0$ limit. This may allow to determine a lowest order term for QCD hadrons which incorporates essential features such as confinement and chiral symmetry breaking, and thus can serve as the starting point of a useful perturbative expansion. I discuss a "Born" (no loop, lowest order in $\hbar$) approximation. Born level states are bound by gauge fields which satisfy the classical field equations. Gauss' law determines a distinct field $A^0(\xv)$ for each instantaneous position of the charges. A Poincaré covariant boundary condition for the gluon field leads to a confining potential for $q\bar q$ and $qqq$ states. In frames where the bound state is in motion the classical gauge field is obtained by a Lorentz boost of the rest frame field.
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