无限红外正则化与Heisenberg代数的状态空间
Infinite Infrared Regularization and a State Space for the Heisenberg Algebra
摘要：
本文给出了一种构造检验函数空间的Krein空间完备化的方法，该完备化具有由比有限阶分布更奇异的核诱导的不定内积.这推广了G.莫尔基奥和F. Strocchi，无限阶奇点的情况。我们给出了局部微分算子和Gelfand-Shilov测试函数空间的条件，以及一个抽象的充分条件。作为一个模型的情况下，我们构建了一个最大正定状态空间的海森堡代数在存在一个无限红外奇点。
英文摘要：
We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand- Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity.
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