不定度量自由场Wick幂级数的谱性质
Spectral Properties of Wick Power Series of a Free Field with an Indefinite Metric
摘要：
研究了两点关联函数具有奇异红外行为且不满足正性条件的自由场的Wick幂级数的性质。如果这些级数被定义在一个适当的泛函域上，那么它们收敛到的域满足伪怀特曼形式主义的所有条件。对于仅收敛于动量表象中的解析测试函数的级数，使用前面介绍的解析泛函的载体锥的概念来制定谱条件。Paley-Wiener-Schwartz定理的一个适当的推广被用来证明这个条件是满足的。
英文摘要：
The properties of infinite series in the Wick powers of a free field whose two-point correlation function has a singular infrared behavior and does not satisfy the positivity condition are investigated. If these series are defined on an appropriate functional domain, then the fields to which they converge satisfy all conditions of the pseudo-Wightman formalism. For series convergent only on analytic test functions in the momentum representation, the spectral condition is formulated using the previously introduced notion of a carrier cone of an analytic functional. A suitable generalization of the Paley-Wiener-Schwartz theorem is used to prove that this condition is satisfied.
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