Quantization of fields with infinite-dimensional invariance groups. III. Generalized Schwinger-Feynman theory
Quantization of fields with infinite-dimensional invariance groups. III. Generalized Schwinger-Feynman theory
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具有无限维不变性群的场的量化。
DOI：
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发表时间：
1962
期刊：
影响因子：
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通讯作者：
B. Dewitt
中科院分区：
文献类型：
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作者：
B. Dewitt
将Schwinger和Feynman的形式方法应用于具有任意高阶初等顶点函数的非线性场论。在本文的前半部分，我们用非正则方法重新推导了我们熟悉的定理。重点放在理论的纯形式方面，这些方面可以期望在推广到标准渐近条件不适用的情况下继续存在。由于假设出现场非线性的背景是一个非阿贝尔无限维不变性群，因此详细讨论了Feynman泛函积分的群不变度量问题。证明了该度量的物理重要性不是由群决定的。论文的后半部分介绍了当引入不变变量时表征系统的传播子和关联函数的理论。证明了一个c-数作用泛函Γ的存在性，它包含了所有量子的完整描述。
The formal methods of Schwinger and Feynman are applied to nonlinear field theories having elementary vertex functions of arbitrarily high order. In the first half of the paper, familiar theorems are rederived by noncanonical methods. Emphasis is given to purely formal aspects of the theory which may be expected to survive generalization to situations in which standard asymptotic conditions are inapplicable. Since the context in which the field nonlinearities are assumed to appear is that of a non‐Abelian infinite‐dimensional invariance group, detailed attention is given to the question of a group invariant measure for the Feynman functional integral. It is shown that the physically important part of the measure is not determined by the group.The second half of the paper is devoted to the theory of the propagators and correlation functions which characterize the system when invariant variables are introduced. The existence of a c‐number action functional Γ which contains a complete description of all quan...