Abstract
A suitable counterterm for a Euclidean space lattice version of ϕ 4n theories, n⩾4, is combined with several additional procedures so that in the continuum limit the resultant quantum field theory is nontrivial. Arguments to support this unconventional choice are presented.
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Fernández, R., Fröhlich, J. and Sokal, A.: Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory, Springer-Verlag, New York, 1992.
Klauder, J.R.: Covariant diastrophic quantum field theory, Phys. Rev. Lett. 28(1972), 769–772;Remarks on nonrenormalizable interactions, Phys. Lett. B 47 (1973), 523-525; Field structure through model studies: aspects of nonrenormalizable theories, Acta Phys. Austriaca, Suppl. XI (1973), 341-387; New measures for nonrenormalizable quantum eld theory, Ann. of Phys. 117 (1979), 19-55.
Fisher, M.E.: The theory of equilibrium critical phenomena, Rep. Progr. Phys. 30(1967), 615–730.
DeFinetti, B.: Theory of Probability, Vol. 2, Wiley, London, 1975.
Klauder, J.R.: Self-interacting scalar elds and (non-)triviality, In: R. Sen and A. Gersten (eds), Mathematical Physics Toward the XXIst Century, Ben-Gurion University Press, Beer Sheva, 1994, pp. 87–98;Poisson distributions and nontriviality of jφ4 theory, Phys. Rev. Lett. 73 (1994), 3051-3054;Nonrenormalizability and nontriviality, In: S. Albeverio et al. (eds), Mathematical Physics and Stochastic Analysis: Essays in Honour of Ludwig Streit, World Scienti c, Singapore, 2000, hep-th/9811181.
Klauder, J.R.: Beyond Conventional Quantization, Cambridge Univ. Press, Cambridge, 2000.
Glimm, J. and Jaffe, A.: Quantum Physics, 2nd edn, Springer, New York, 1987.
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Klauder, J.R. Overcoming Nonrenormalizability. Letters in Mathematical Physics 63, 229–239 (2003). https://doi.org/10.1023/A:1024407001695
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DOI: https://doi.org/10.1023/A:1024407001695