Isgur-Wise函数，Bjorken-Uraltsev求和规则及其洛伦兹群解释，纪念尼古拉·乌拉尔采夫
Isgur-Wise functions, Bjorken-Uraltsev Sum Rules and their Lorentz group interpretation, In Memoriam Nikolai Uraltsev
摘要：
在QCD的重夸克极限下，利用Nikolai Uraltsev提出的算子乘积展开和非前向振幅，我们得到了推广Bjorken和Uraltsev求和规则的求和规则.我们恢复Uraltsev下限的Isgur-明智（IW）的功能，我们推广到更高的衍生物的斜率。我们表明，这些结果有一个明确的解释，在洛伦兹群，因为IW函数是由重叠的初始和最终的光云，相关的洛伦兹变换。洛伦兹群和求和规则方法都是等价的。此外，我们制定了一个积分表示的IW函数的正测度。反转这个积分公式，我们得到的措施，在IW函数，允许制定标准，以决定是否一个给定的IW函数是兼容的或不与求和规则的约束。我们比较这些理论的限制，在文献中提出的一些形式。
英文摘要：
In the heavy quark limit of QCD, using the Operator Product Expansion and the non-forward amplitude, as proposed by Nikolai Uraltsev, we formulate sum rules that generalize Bjorken and Uraltsev sum rules. We recover the Uraltsev lower bound for the slope of the Isgur-Wise (IW) function, that we generalize to higher derivatives. We show that these results have a clear interpretation in terms of the Lorentz group, since the IW function is given by an overlap between the initial and final light clouds, related by Lorentz transformations. Both the Lorentz group and the Sum Rules approach are equivalent. Moreover, we formulate an integral representation of the IW function with a positive measure. Inverting this integral formula, we obtain the measure in terms of the IW function, allowing to formulate criteria to decide if a given ansatz for the IW function is compatible or not with the sum rule constraints. We compare these theoretical constraints to some forms proposed in the literature.
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