Weak Adiabatic Limit in Quantum Field Theories with Massless Particles
Weak Adiabatic Limit in Quantum Field Theories with Massless Particles
复制标题
无质量粒子量子场论中的弱绝热极限
DOI：
10.1007/s00023-018-0652-z
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
P. Duch
中科院分区：
文献类型：
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作者：
P. Duch
在爱泼斯坦-格拉泽框架下，我们在四维Minkowski空间中构造了一大类微扰QFT模型中的Wightman函数和Green函数。为此，我们证明了弱绝热极限的存在性，推广了Blanchard和Seneor的结果。在假设时序乘积满足一定的正规化条件下，我们的证明是有效的。我们证明了这一归一化条件可以应用于所有相互作用顶点为正则维4的模型以及所有相互作用顶点为正则维3的模型中，只要每个模型都包含至少一个重量场。此外，我们还证明了它与通常施加在时序乘积上的所有标准归一化条件是相容的。例如，这一结果适用于量子电动力学和非阿贝尔杨-米尔斯理论。
We construct the Wightman and Green functions in a large class of models of perturbative QFT in the four-dimensional Minkowski space in the Epstein–Glaser framework. To this end we prove the existence of the weak adiabatic limit, generalizing the results due to Blanchard and Seneor. Our proof is valid under the assumption that the time-ordered products satisfy certain normalization condition. We show that this normalization condition may be imposed in all models with interaction vertices of canonical dimension 4 as well as in all models with interaction vertices of canonical dimension 3 provided each of them contains at least one massive field. Moreover, we prove that it is compatible with all the standard normalization conditions which are usually imposed on the time-ordered products. The result applies, for example, to quantum electrodynamics and non-abelian Yang–Mills theories.