流形上的马尔可夫量子场
Markov quantum fields on a manifold
摘要：
研究紧致流形上的标量量子场论。自由理论是用泛函积分来定义的。对于正质量，它被证明具有纳尔逊意义下的马尔可夫性质。当流形具有反射对称性时，此属性用于建立反射正性结果。在维数d=2，我们使用马尔可夫性质建立缝合操作的流形边界圆。在d=2时，证明了相互作用场的马尔可夫性质.
英文摘要：
We study scalar quantum field theory on a compact manifold. The free theory is defined in terms of functional integrals. For positive mass it is shown to have the Markov property in the sense of Nelson. This property is used to establish a reflection positivity result when the manifold has a reflection symmetry. In dimension d=2 we use the Markov property to establish a sewing operation for manifolds with boundary circles. Also in d=2 the Markov property is proved for interacting fields.
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