An alternate constructive approach to the φ 43 quantum field theory , and a possible destructive approach to φ
An alternate constructive approach to the φ 43 quantum field theory , and a possible destructive approach to φ
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2018
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通讯作者：
A. Sokal
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作者：
A. Sokal
我研究了用格点近似构造cp 4量子场论。证明连续统极限的存在性很容易（通过连续性）;关键问题是这个极限是否是（广义）自由场以外的东西。我使用相关不等式，红外边界和场方程来研究这个问题。对于时空维d小于4，我给出了一个简单的证明，连续极限理论确实是非平凡的;然而，它依赖于一个与Glimm和Jaffe的T6猜想密切相关的相关不等式。此外，连续统理论的欧几里德不变性是本方法中的一个开放性问题。对于时空维度d大于或等于4，我认为，但不证明，连续极限是不可避免的（广义）自由场，无论选择的电荷重整化。该论点是基于旧的想法的朗道和Pomeranchuk，通过使用相关不等式适用于精确的字段方程改进。简历在研究cp 4理论的构造时，champs把网格近似的Au moyen量化.本文是对一个博士论文的稍加修改的版本。论文提交给普林斯顿大学物理系（1981年1月）。这项研究得到了NSF资助PHY 78-23952的部分支持。Annales de l'Institut Henri Poincare-Section A-B. XXXVII，0020-2339/1 982/3 1 7/$5，00/ © Gauthier-Villars '
I study the construction of cp4 quantum field theories by means of lattice approximations. It is easy to prove the existence of the continuum limit (by subsequences) ; the key question is whether this limit is something other than a (generalized) free field. I use correlation inequalities, infrared bounds and field equations to investigate this question. For space-time dimension d less than four, I give a simple proof that the continuum-limit theory is indeed nontrivial ; it relies, however, on a conjectured correlation inequality closely related to the T6 conjecture of Glimm and Jaffe. Moreover, the Euclidean invariance of the continuum theory is an open question within the present approach. For space-time dimension d greater than or equal to four, I argue but do not prove that the continuum limit is inevitably a (generalized) free field, irrespective of the choice of charge renormalization. The argument is based on old ideas of Landau and Pomeranchuk, improved through the use of correlation inequalities applied to the exact field equations. RESUME. On etudie la construction des theories cp4 des champs quantifies au moyen de l’approximation du reseau. On demontre facilement (*) This paper is a slightly revised version of a Ph. D. thesis presented to the physics department at Princeton University (January 1981). The research was supported in part by NSF grant PHY 78-23952. Annales de l’lnstitut Henri Poincare-Section A-Vol. XXXVII, 0020-2339/1 982/3 1 7/$ 5,00/ © Gauthier-Villars ’