Abstract
The functional equations of a renormalization group are formulated for theories for dimensional coupling constants. The structure of the general solutions of the equation is determined for an invariant charge. Particular attention is paid to models with a negative mass dimensionality of the coupling constants (i.e., to models which are unrenormalizable in ordinary perturbation theory). The correspondence between the general solutions in the UV region with ordinary perturbation theory leads to nonanalyticity in terms of the coupling constant. An additional assumption that the number of invariant charges is finite leads to limitations on the parameters of the Bogolyubov R operation. The possibility of scale invariance at small distances is discussed. As an illustration of these hypotheses, an exactly solvable unrenormalizable nonrelativistic model is analyzed.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 23–29, December, 1974.
The authors thank N. N. Bogolyubov, I. F. Ginzburg, A. T. Filippov, B. V. Medredev, M. K. Polivanov, and A. N. Tavkhelidze for interesting discussions.
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Blokhintsev, D.I., Efremov, A.V. & Shirkov, D.V. Renormalization group in unrenormalizable field theory. Soviet Physics Journal 17, 1650–1655 (1974). https://doi.org/10.1007/BF00892873
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DOI: https://doi.org/10.1007/BF00892873