Convergence of the Sum Rules for Cluster Functions in a <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>3</mn></mrow></msup></mrow></math></span> Ladder Model

Fritz W. Bopp

doi:10.1103/PhysRevD.7.465

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Convergence of the Sum Rules for Cluster Functions in a $φ^{3}$ Ladder Model

Fritz W. Bopp

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

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Phys. Rev. D 7, 465 – Published 15 January, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.465

Abstract

The convergence of the series in the sum rules of Campbell and Chang for cluster functions is investigated numerically for the $φ^{3}$ ladder model. It is found that in this model these sum rules diverge for a sufficiently large value of the coupling constant that the Pomeranchukon-Regge trajectory goes through $α (0) = 1$ .

References (5)

K. Huang, Statistical Mechanics (Wiley, New York, 1963)
D. K. Campbell and S.-J. Chang, Phys. Rev. D 4, 1151 (1971) ibid.4, 3658 (1971) Univ. of Illinois Report No. ILL-(TH)-71-11 (unpublished) D. K. Campbell, Phys. Rev. D 6, 2658 (1972)
A. H. Mueller, Phys. Rev. D 4, 150 (1971) S.-J. Chang, T.-M. Yang, and Y.-P. Yao, ibid. 5, 271 (1972)
H. W. Wyld, Phys. Rev. D 3, 3090 (1971)
D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962) L. Bertocchi, S. Fubini, and M. Tonin, ibid. 25, 626 (1962)

[c1] K. Huang, Statistical Mechanics (Wiley, New York, 1963)

[c2] D. K. Campbell and S.-J. Chang, Phys. Rev. D 4, 1151 (1971) ibid.4, 3658 (1971) Univ. of Illinois Report No. ILL-(TH)-71-11 (unpublished) D. K. Campbell, Phys. Rev. D 6, 2658 (1972)

[c3] A. H. Mueller, Phys. Rev. D 4, 150 (1971) S.-J. Chang, T.-M. Yang, and Y.-P. Yao, ibid. 5, 271 (1972)

[c4] H. W. Wyld, Phys. Rev. D 3, 3090 (1971)

[c5] D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962) L. Bertocchi, S. Fubini, and M. Tonin, ibid. 25, 626 (1962)

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Convergence of the Sum Rules for Cluster Functions in a $φ^{3}$ Ladder Model

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Convergence of the Sum Rules for Cluster Functions in a φ3 Ladder Model

Abstract

References (5)

Convergence of the Sum Rules for Cluster Functions in a $φ^{3}$ Ladder Model