2012/01/29 by Arthur Jaffe, Jaffe, Arthur, Christian D. Jäkel +3 · 1 citation
Arts and Humanities · Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Philosophy and History of Science #Quantum Mechanics and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1201.6003
openalex publication_date 2012/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our method generalizes Osterwalder and Schrader's construction of Euclidean fields. We allow complex-valued classical fields in the case of quantum field theories that describe neutral particles. From an analytic point-of-view, the key to using our method is reflection positivity. We investigate conditions on the Fourier representation of the fields to ensure that reflection positivity holds. We also show how reflection positivity is preserved by various space-time compactifications of Euclidean space.