Markov quantum fields on a manifold

Details Markov quantum fields on a manifold Markov quantum fields on a manifold

2003-05-08

arxiv.org/abs/math-ph/0305017v1

Rev.Math.Phys. 16 (2004) 243-256

Physics

Mathematical Physics

14 pages, 1 figure, Latex

Scientific paper

10.1142/S0129055X04001947

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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