The Nonlinear $\sigma$ Model in the Loop Expansion
The Nonlinear $\sigma$ Model in the Loop Expansion
复制标题
循环展开中的非线性$sigma$模型
DOI：
10.1103/physrevd.23.425
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发表时间：
1981
影响因子：
5
通讯作者：
C. Bernard
中科院分区：
文献类型：
--
作者：
T. Appelquist;C. Bernard
在环展开的背景下，讨论了四维非线性sigma模型。由于模型是摄动不可重整的，非拉格朗日形式的散度当然是预期的；也许令人惊讶的是，在原来的非线性对称下，有一些散度似乎不是不变的。然而，我们证明了这些明显的非不变项对质量壳量没有贡献，并且可以通过涉及时空导数的场重新定义逐级消除。然后详细检查了线性西格玛模型；它显示了非线性模型，包括明显的非不变项，是如何在sigma质量趋于无穷时作为线性模型的极限出现的。最后，我们将我们的方法与非线性模型中“非不变”项的其他处理方法进行比较。
The nonlinear sigma model in four dimensions is discussed in the context of the loop expansion. Since the model is perturbatively nonrenormalizable, divergences not of the form of the Lagrangian are of course expected; what is perhaps surprising is that there are divergences which appear not to be invariant under the original nonlinear symmetry. We demonstrate, however, that these apparently noninvariant terms do not contribute to on-mass-shell quantities and may be eliminated order by order by a field redefinition involving space-time derivatives. The linear sigma model is then examined in detail; it is shown how the nonlinear model, including the apparently noninvariant terms, emerges as the limit of the linear model as the sigma mass goes to infinity. Finally, we compare our approach with other treatments of the ''noninvariant'' terms in the nonlinear model.