Abstract
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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Acknowledgements
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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Communicated by Karl-Henning Rehren.
Research partially supported by CUNY CCR Grant No. 1510.
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Zahariev, S. Infinite Volume Limits in Euclidean Quantum Field Theory via Stereographic Projection. Ann. Henri Poincaré 19, 3267–3287 (2018). https://doi.org/10.1007/s00023-018-0709-z
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DOI: https://doi.org/10.1007/s00023-018-0709-z