Renormalization of the coupled cluster equations in three-dimensional <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>φ</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math></span> quantum field theory

Ulrich Kaulfuss

doi:10.1103/PhysRevD.32.1421

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Renormalization of the coupled cluster equations in three-dimensional $φ^{4}$ quantum field theory

Ulrich Kaulfuss

Institut fuer Theoretische Physik II, Ruhr-Universitaet Bochum, 4630 Bochum, West Germany

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Phys. Rev. D 32, 1421 – Published 15 September, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.1421

Abstract

We construct eigenstates of the ( $φ^{4}$ $)_{3}$ quantum field theory in the framework of the coupled cluster method (CCM). Therefore the principle of coherence is stressed leading to a description of these states by an infinite set of correlation amplitudes. In the standard form of the CCM the amplitudes obey a hierarchy of coupled nonlinear integral equations containing some poorly defined terms because of ultraviolet divergences. We remove these divergences by a systematic transformation to an equivalent set of amplitudes. No expansion in the coupling constant is therefore required to make the hierarchy well defined. It is possible to find truncation schemes for the transformed amplitudes which are compatible with the requirement of renormalizability. We conclude that the CCM is helpful to analyze the structure of the vacuum and to make precise statements about the mass spectrum of superrenormalizable quantum field theories.

References (16)

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C. S. Hsue, H. Kümmel and P. Ueberholz, following paper, Phys. Rev. D 32, 1435 (1985).
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H. Kümmel, in Proceedings of the 3rd International Conference on Recent Progress in Many Body Theory, Oaxtepec, Mexico, 1981, edited by J. G. Zabolitzky (Springer, Berlin, 1981).
R. Offermann, H. Kümmel and W. Ey, Nucl. Phys. A273, 349 (1976).
M. Gell-Mann and F. Low, Phys. Rev. 84, 35 (1951).
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S. J. Chang, Phys. Rev. D 12, 1071 (1975).
S. F. Magruder, Phys. Rev. D 14, 1602 (1976).
C. S. Hsue and C. L. Lin (unpublished).
H. Kümmel, Nucl. Phys. A317, 199 (1979).
E. C. G. Stueckelberg, Phys. Rev. 81, 130 (1951).
K. Symanzik, Nucl. Phys. B190, 1 (1981).
H. Kümmel and M. Funke (in preparation).

[c1] F. Coester and H. Kümmel, Nucl. Phys. 17, 477 (1960); H. Kümmel, K. H. Lührmann and J. G. Zabolitzky, Phys. Rep. 36C, 1 (1978).

[c2] K. Emrich and J. G. Zabolitzky, Phys. Rev. B 30, 2049 (1984).

[c3] C. S. Hsue, H. Kümmel and P. Ueberholz, following paper, Phys. Rev. D 32, 1435 (1985).

[c4] R. Haag, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 29, 12 (1955).

[c5] J. Froehlich, B. Simon and T. Spencer, Commun. Math. Phys. 50, 79 (1976).

[c6] H. Kümmel, in Proceedings of the 3rd International Conference on Recent Progress in Many Body Theory, Oaxtepec, Mexico, 1981, edited by J. G. Zabolitzky (Springer, Berlin, 1981).

[c7] R. Offermann, H. Kümmel and W. Ey, Nucl. Phys. A273, 349 (1976).

[c8] M. Gell-Mann and F. Low, Phys. Rev. 84, 35 (1951).

[c9] H. Kümmel, Nucl. Phys. A176, 205 (1971).

[c10] S. J. Chang, Phys. Rev. D 12, 1071 (1975).

[c11] S. F. Magruder, Phys. Rev. D 14, 1602 (1976).

[c12] C. S. Hsue and C. L. Lin (unpublished).

[c13] H. Kümmel, Nucl. Phys. A317, 199 (1979).

[c14] E. C. G. Stueckelberg, Phys. Rev. 81, 130 (1951).

[c15] K. Symanzik, Nucl. Phys. B190, 1 (1981).

[c16] H. Kümmel and M. Funke (in preparation).

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Renormalization of the coupled cluster equations in three-dimensional $φ^{4}$ quantum field theory

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Renormalization of the coupled cluster equations in three-dimensional φ4 quantum field theory

Abstract

References (16)

Renormalization of the coupled cluster equations in three-dimensional $φ^{4}$ quantum field theory