MARKOV QUANTUM FIELDS ON A MANIFOLD
- 1 March 2004
- journal article
- Published by World Scientific Pub Co Pte Ltd in Reviews in Mathematical Physics
- Vol. 16 (2), 243-255
- https://doi.org/10.1142/s0129055x04001947
Abstract
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.Keywords
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