QCD_2：'t Hooft方程与相对论薛定谔方程
QCD_2: 't Hooft equation vs. relativistic Schroedinger equation
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中文总结 AI 辅助
本文比较了二维QCD中通过Bethe-Salpeter方程和相对论薛定谔方程计算介子质量的两种方法，发现领头半经典近似一致，但预渐近WKB修正不同，基态差异显著，高激发态差异迅速减小。
中文摘要 AI 辅助
我们讨论具有质量m的基本夸克的二维QCD，在't Hooft极限下（N→∞，g²→0，g²N=常数）。该理论的谱包含一系列介子态。这些态的质量可以通过求解适当的积分Bethe-Salpeter方程来评估。另一种简单的做法是求解相对论哈密顿量Ĥ=2√(p̂²+m²)+σ|x|的薛定谔方程，其中弦张力σ=g²N/4。我们比较了这两种方法得到的结果。在领头半经典近似下，它们一致。然而，我们表明，通过这两种方式计算的质量的预渐近WKB修正项是不同的。对于基态，它们起着重要作用。但已经对于n=3，两种预测之间的相对差异不超过2.5%，并且随着n的增加而迅速下降。
英文摘要
We discuss 2-dimensional $QCD$ with a fundamental quark of mass $m$ in the 't Hooft limit ($N \to \infty, \, g^2 \to 0, \, g^2N =$ const). The spectrum of this theory includes a chain of meson states. The masses of these states can be evaluated by solving the proper integral Bethe-Salpeter equation. An alternative simple procedure consists in solving the Schrödinger equation for the relativistic Hamiltonian $$ \hat H\ =\ 2\sqrt{\hat p^2 + m^2} + σ|x| $$ with the string tension $σ= g^2N/4$. We compare the results obtained by these two methods. In the leading semiclassical approximation, they coincide. We show, however, that the preasymptotic WKB corrections to the masses calculated in these two ways are different. For the ground state, they play an essential role. But already for $n=3$, the relative difference between the two predictions does not exceed 2.5\% and rapidly falls off as $n$ increases.
发表机构
- SUBATECH（SUBATECH研究所）
- Université de Nantes（南特大学）
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