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Prog. Theor. Phys. Vol. 84 No. 2 (1990) pp. 324-330
Remarks on Quantized Hamiltonians in the SU(2) Skyrme Model
Azuma Toda
Department of Applied Physics, Tohoku Gakuin University, Tagajo 985
(Received February 22, 1990)
Abstract:
We examine the quantization procedure of SU(2) Skyrme model and present the two different quantized Hamiltonians. One effectively takes the same form as the usual one. The other has an additive term. We suggest that the Skyrme Hamiltonian, for the empirical value of fπ=186 MeV, must require another contribution to the static part.
URL :
http://ptp.ipap.jp/link?PTP/84/324/
DOI : 10.1143/PTP.84.324
References:
- T. H. R. Skyrme, Proc. R. Soc. A260 (1961), 127.
For a review article, see I. Zahed and G. E. Brown, Phys. Rep. 142 (1986), 1[CrossRef].
- G.'t Hooft, Nucl. Phys. B72 (1974), 461; ibid. B75 (1974), 461.
- E. Witten, Nucl. Phys. B160 (1979), 57.
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See also Solitons in Nuclear and Elementary Particle Physics, ed. A. Chodos, E. Hadjimichael and C. Tze (World Scientific, Singapore, 1984).
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M. Chemtob, Nuovo Cim. A89 (1985), 381.
H. Yabu and K. Ando, Nucl. Phys. B301 (1988), 601.
See also the relevant references cited therein.
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For other possibilities, see K. Fujii, K. Sato, N. Toyota and A. Kobushkin, Phys. Rev. Lett. 58 (1987), 651[APS]; A. Kanazawa, Prog. Theor. Phys. 77 (1987), 212[PTP].
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K. Fujii, A. Kobushkin, K. Sato and N. Toyota, Phys. Rev. D35 (1987), 1896[APS].
K. Fujii, K. Sato and N. Toyota, Phys. Rev. D37 (1988), 3663[APS].
A. Kanazawa, Prog. Theor. Phys. 77 (1987), 1240[PTP].
And Ref. 6). Fujii et al. give no comment on the numerical value of ΔM. We cannot expect a large value of ΔM. Kanazawa introduces the quantum term with a free parameter (ΔH) into his scheme. We suspect that his scheme must destroy the physical picture of quantum fluctuations around the classical soliton solution.
- See, e.g., Zahed and Brown (Ref. 1)).
- See, Chemtob (Ref. 5)), Yabu and Ando (Ref. 5)), Fujii et al. (Refs. 6) and 7)) and Kanazawa (Ref. 7)).
As for a general treatment, see R. Marnelius, Nucl. Phys. B142 (1978), 108.
- See, e.g., T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, New York, 1981), p. 476.
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See, e.g., N. H. Christ and T. D. Lee, Phys. Rev. D12 (1975), 1606[APS].
- See, e.g., J. M. Normand, A Lie Group: Rotations in Quantum Mechanics (North-Holland, Amsterdam, 1980), p. 67.
- E. Guadagnini, Nucl. Phys. B236 (1984), 35.
- J. M. Normand (Ref. 12)), p. 114.
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After completion of this work, we noticed a paper with a discontinuous derivative \dotφ(r), which effectively modifies the static part. See M. Lacombe, B. Loiseau, R. Vinh Mau and W. N. Cottingham, Phys. Rev. D40 (1989), 3012[APS].
