Annales Henri Poincaré

, Volume 19, Issue 11, pp 3267–3287 | Cite as

Infinite Volume Limits in Euclidean Quantum Field Theory via Stereographic Projection

  • Svetoslav Zahariev


We present a general infinite volume limit construction of probability measures obeying the Glimm–Jaffe axioms of Euclidean quantum field theory in arbitrary space–time dimension. In particular, we obtain measures that may be interpreted as corresponding to scalar quantum fields with arbitrary bounded continuous self-interaction. It remains, however, an open problem whether this general construction contains non-Gaussian measures.


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The author is grateful toWojciech Dybalski, Leonard Gross, NikolayM. Nikolov and Yoh Tanimoto for many helpful suggestions and stimulating discussions at various stages of this project.


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Authors and Affiliations

  1. 1.MEC DepartmentLaGuardia Community College of The City University of New YorkLong Island CityUSA

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