Abstract
The unitary relativistic model of quantum field theory with rapidly increasing spectral function (i.e. it grows faster than any finite power of momentum) is investigated. It is shown that there exist nontrivial Lagrangians, leading to this kind of spectral functions and allowing to construct the local theory without the ultraviolet divergences on their basis. In this theory theS-matrix is unitary and not equal identically to unity.
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References
Feinberg, G., andA. Pais: Phys. Rev.131, 2724 (1963);133, B477 (1964).
Pradhau, T.: Nucl. Phys.43, 11 (1963).
Schroer, B.: J. Math. Phys.5, 1361 (1964),7, 10 (1966).
Sawyer, R. F.: Phys. Rev.134, B448 (1964).
Klaiber, B.: Nuovo Cimento36, 165 (1965).
Arbuzov, B. A., andA. T. Filippov: Nuovo Cimento38, 796 (1965); Phys. Lett.13, 95 (1964).
Guttinger, W.: Fortschr. Physik14, 8/9 (1966).
Blokhintsev, D. I.: Intern. Conf. on High Energy Phys. at CERN 687 (1962).
Efimov, G. V.: JETP44, 2107 (1963); Nuovo Cimento32, 1046 (1964); Nucl. Phys.74, 657 (1965).
Volkov, M. K., andG. V. Efimov: JETP47, 1800 (1964).
Fradkin, E. S.: Nucl. Phys.49, 624 (1963).
Meiman, N. N.: JETP47, 1966 (1964).
Jaffe, A.: Phys. Rev. Lett.17, 661 (1966).
Volkov, M. K.: Yadern. Fiz. II, 171 (1965).
Yadern. Fiz.6, 1100 (1967). Preprint JINR P2-3270, Dubna (1967).
-- Preprint E2-3266, Dubna (1967). [Yadern. Fiz. 7, 445 (196*)].
Erdelyi, A. (Ed.): Higher transcendental functions, vol. 1. New York-Toronto-London: Mc Crow-Hill Book Company, Inc. 1953.
Bogolubov, N. N., andD. V. Shirkov: Introduction to the theory of quantized fields. New York: Addison Wesley, 1959.
Kolkunov, V. A.: JETP43, 1448 (1962).
Okubo, S.: Nuovo Cimento19, 574 (1961).
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Volkov, M.K. Quantum field model with unrenormalizable interaction. Commun.Math. Phys. 7, 289–304 (1968). https://doi.org/10.1007/BF01646662
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DOI: https://doi.org/10.1007/BF01646662