Schwinger functions and their generating functionals. II. Markovian and generalized path space measures on J
Schwinger functions and their generating functionals. II. Markovian and generalized path space measures on J
复制标题
施温格函数及其生成泛函。
DOI：
10.1016/0001-8708(77)90119-0
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发表时间：
1977
影响因子：
1.7
通讯作者：
J. Fröhlich
中科院分区：
文献类型：
--
作者：
J. Fröhlich
给出了Schwartz分布空间J′上的J-拟不变、马尔可夫和广义路空间测度的一般理论.研究了在量子场论感兴趣的J′的不同变换群作用下这类测度的遍历性。因此，马尔可夫场理论的代数方法和一般的概率（欧几里德）框架的研究自发对称性破缺和相变的量子场模型，涉及基本标量场，如E144模型（或广义汤川模型在两个时空维度）。给出了这些结果在P（ψ）2量子场模型中的应用，并严格证明了这些模型在每个纯相中的短程行为是正则的，而长程行为由物理质量决定.
A general theory of J-quasi-invariant, Markovian, and generalized path space measures on the Schwartz distribution space J′ is developed. Ergodicity properties of such measures under the action of different transformation groups of J′ of interest to quantum field theory are studied. As a result an algebraic approach to Markov field theory and a general, probabilistic (Euclidcan) framework for the study of spontaneous symmetry breaking and phase transitions in quantum field models involving fundamental scalar fields such as the ø 4-model (or the generalized Yukawa model in two space-time dimensions) are presented. Applications of these results to the P (ø) 2 quantum field models are given and it is rigorously proven that the short-distance behavior of these models in each pure phase is canonical and the long-distance behavior is determined by the physical mass.