Abstract
We discuss the problem of rigorously constructing the continuum limit in the fermionic hierarchical model. The continuum limit constructed as the limit of fields on the refined hierarchical lattices is a field on a p-adic continuum. We investigate the problem of reconstructing the coupling constants of the continuum model from the coupling constants of the discretized model.
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É. Yu. Lerner and M. D. Missarov,Theor. Math. Phys.,78, 177 (1989).
E. Yu. Lerner and M. D. Missarov,Commun. Math. Phys.,121, 35 (1989).
P. M. Bleher and Ya. G. Sinai,Commun. Math. Phys.,33, 23 (1973).
P. Collet and J.-P. Eckmann,A Renormalization Group Analysis of the Hierarchical Model in Statistical Mechanics, Springer, Berlin (1978).
Ya. G. Sinai,Theory of Phase Transitions: Rigorous Results [in Russian], Nauka, Moscow (1980); English transl., Pergamon, Oxford (1982).
P. M. Bleher and P. Major,Ann. Prob.,15, 431 (1987).
V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov,p-Adic Analysis and Mathematical Physics [in Russian], Nauka, Moscow (1994); English transl., World Scientific, Singapore (1994).
L. Brekke and P. G. O. Freund,Phys. Rep.,233, 1 (1993).
E. Yu. Lerner and M. D. Missarov,J. Stat. Phys.,76, 805 (1994).
E. Yu. Lerner and M. D. Missarov,Theor. Math. Phys.,107, 579 (1996).
M. D. Missarov,Theor. Math. Phys.,114, 255 (1998).
J. Glimm and A. Jaffe,Quantum Physics: A Functional Integral Point of View, Springer, Berlin (1981).
K. Gawedzki and A. Kupiainen,Commun. Math. Phys.,99, 197 (1985).
K. Gawedzki and A. Kupiainen,Commun. Math. Phys.,102, 1 (1985).
J. Feldman, J. Magnen, V. Rivasseu, and R. Seneor,Commun. Math. Phys.,103, 67 (1986).
T. C. Dorlas,Commun. Math. Phys.,136, 169 (1991).
M. D. Missarov,Lett. Math. Phys.,32, 347 (1994).
V. I. Arnold,Geometrical Methods in the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1978); English transl., Springer, Berlin (1983).
I. M. Gelfand, M. I. Graev, and I. I. Pyatetskii-Shapiro,Representation Theory and Automorphic Functions [in Russian], Nauka, Moscow (1966); English transl., Saunders, Philadelphia (1969).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 1, pp. 40–50, January, 1999.
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Missarov, M.D. Continuum limit in the fermionic hierarchical model. Theor Math Phys 118, 32–40 (1999). https://doi.org/10.1007/BF02557193
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DOI: https://doi.org/10.1007/BF02557193