标题： 关于规范理论中规范固定的一点说明 显示英文标题

标题： Note on the Gauge Fixing in Gauge Theory

摘要： 在没有Gribov复杂性的情况下，规范理论中的修正规范固定$ \int{\cal D}A_{\mu}\{\exp[-S_{YM}(A_{\mu})-\int f(A_{\mu})dx] /\int{\cal D}g\exp[-\int f(A_{\mu}^{g})dx]\}$，例如$f(A_{\mu})=(1/2)(A_{\mu})^{2}$，如果考虑到规范场沿整个规范轨道的变化，就与传统的Faddeev-Popov公式$\int{\cal D}A_{\mu}\{\delta(D^{\mu}\frac{\delta f(A_{\nu})}{\delta A_{\mu}})/\int {\cal D}g\delta(D^{\mu}\frac{\delta f(A_{\nu}^{g})} {\delta A_{\mu}^{g}})\}\exp[-S_{YM}(A_{\mu})]$相同。尽管外观差异很大，修正后的公式定义了一个局部的且BRST不变的理论，因此至少在微扰理论中确保了单位性。在存在Gribov复杂性的情况下，如非微扰Yang-Mills理论中所预期的，修正公式等价于传统公式，但并不完全相同：两种定义通常会导致非局部理论，因此单位性并不明显。对格点正则化的含义进行了简要讨论。 显示英文摘要

摘要： In the absence of Gribov complications, the modified gauge fixing in gauge theory $ \int{\cal D}A_{\mu}\{\exp[-S_{YM}(A_{\mu})-\int f(A_{\mu})dx] /\int{\cal D}g\exp[-\int f(A_{\mu}^{g})dx]\}$ for example, $f(A_{\mu})=(1/2)(A_{\mu})^{2}$, is identical to the conventional Faddeev-Popov formula $\int{\cal D}A_{\mu}\{\delta(D^{\mu}\frac{\delta f(A_{\nu})}{\delta A_{\mu}})/\int {\cal D}g\delta(D^{\mu}\frac{\delta f(A_{\nu}^{g})} {\delta A_{\mu}^{g}})\}\exp[-S_{YM}(A_{\mu})]$ if one takes into account the variation of the gauge field along the entire gauge orbit. Despite of its quite different appearance,the modified formula defines a local and BRST invariant theory and thus ensures unitarity at least in perturbation theory. In the presence of Gribov complications, as is expected in non-perturbative Yang-Mills theory, the modified formula is equivalent to the conventional formula but not identical to it:Both of the definitions give rise to non-local theory in general and thus the unitarity is not obvious. Implications of the present analysis on the lattice regularization are briefly discussed.