2007/09/30 by Z. Haba · 2 citations
Mathematics · Physics and Astronomy · #Analytic continuation #Black Holes and Theoretical Physics #Continuation #Cosmology and Gravitation Theories #Dimensional reduction #Euclidean distance matrix #Euclidean domain #Euclidean geometry #Field (mathematics) #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Product (mathematics) #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum field theory #Quantum mechanics #Remainder #Zero (linguistics) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/25/7/075005
published in Classical and Quantum Gravity 25(7), 075005 (IOP Publishing) · 17 pages
arxiv created 2008/02/15 · openalex publication_date 2008/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss Euclidean Green functions on product manifolds . We show that if is compact and is not compact then the Euclidean field on can be approximated by its zero mode which is a Euclidean field on . We estimate the remainder of this approximation. We show that for large distances on the remainder is small. If , where S β is a circle of radius β, then the result reduces to the well-known approximation of the D -dimensional finite temperature quantum field theory by ( D − 1)-dimensional one in the high-temperature limit. Analytic continuation of Euclidean fields is discussed briefly.