Abstract
Nonlinear effective Lagrangian models with a chiral symmetry have been used to describe strong interactions at low energy, for a long time. The Skyrme model and the chiral quark-meson model are two such models, which have soliton solutions which can be identified with the baryons. We describe the various kinds of soliton states in these nonlinear models and discuss their physical significance and uses in this review. We also study these models from the view point of classical nonlinar dynamical systems. We consider fluctuations around theB=1 soliton solutions of these models (B, being the baryon number) and solve the spherically symmetric, time-dependent systems. Numerical studies indicate that the phase space around the Skyrme soliton solution exhibits spatio-temporal chaos. It is remarkable that topological solitons signifying stability/order and spatio-temporal chaos coexist in this model. In contrast with this, the soliton of the quark-meson model is stable even for large perturbations.
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References
See for example, R Rajaraman, Solitons and Instantons (North Holland Publishing Company, Amsterdam, 1982) and references therein
J Hong, Y Kim and P Y Pac,Phys. Rev. Lett. 64, 2230 (1990)
R Jackiw and E J Weinberg,Phys. Rev. Lett. 64, 2234 (1990)
W A Bardeen, S D Drell, M Weinstein and T M Yan,Phys. Rev. D11, 1094 (1975)
R Friedberg and T D Lee,Phys. Rev. D16, 1096 (1977);D17, 2623 (1978)
T H R Skyrme,Proc. R. Soc. Am. A260, 127 (1961)
V G Makhankov, Y P Ryabkov, and V I Sanyuk,The Skyrme Model (Springer Verlag, Berlin, Heidelberg, 1993)
E Witten,Nucl. Phys. B223, 433 (1983); in this paper, essential use is made of the Wess-Zumino term given by J Wess and B Zumino,Phys. Lett. B37, 95 (1971)
A P Balachandran,Lectures at 1985 TASI edited by M Bowick and F Gursey (World Scientific, Singapore, 1986)
V B Kopeliovich and B E Shtern,JETP. Lett. 45, 203 (1987)
E Braaten and L Carson,Phys. Rev. D38, 3525 (1988)
A P Balachandran, A Barducci, F Lizzi, V G J Rodgers and A Stern,Phys. Rev. Lett. 52, 887 (1984)
Faheem Hussain and M S Sriram,Phys. Rev. Lett. 55, 1169 (1985)
M P Mattis and M Karliner,Phys. Rev. D31, 2833 (1985)
M P Mattis and M Peskin,Phys. Rev. D32, 58 (1985)
A Jackson, A D Jackson and V Pasquier,Nucl. Phys. A432, 562 (1985)
R D Ball,Int. J. Mod. Phys. A23, 4391 (1990)
S Kahana, G Ripka and V Soni,Nucl. Phys. A415, 351 (1984)
M C Birse and M K Banerjee,Phys. Rev. D31, 118 (1984)
J Segar, M Sripriya and M S Sriram,Int. J. Mod. Phys. E3, 769 (1994)
J Segar, M Sripriya and M S Sriram,Phys. Lett. B342, 201 (1995)
S G Matinyan, G K Savvidy and N G T Savvidy,Zh. Eksp. Teor. Fiz. 80, 830 (1981) [Sov. Phys. JETP. 53, 421 (1981)]
A Giansanti and P D Simic,Phys. Rev. D38, 1352 (1988)
C N Kumar and A Khare,J. Phys. A22, L849 (1989)
B Dey, C N Kumar and A Sen,Int. J. Mod. Phys. A8, 1755 (1993)
B A Bambah, S Lakshmibala, C Mukku and M S Sriram,Phys. Rev. D47, 4677 (1993)
M S Sriram, C Mukku, S Lakshmibala and B A Bambah,Phys. Rev. D49, 4246 (1994)
S Lakshmibala, inComputational aspects in chaos and nonlinear dynamics edited by G Ambika and V M Nandakumaran (Wiley Eastern, New Delhi, 1994) pp. 37–47
C Mukku, M S Sriram, J Segar, B A Bambah and S Lakshmibala, submitted for publication S Lakshmibala, B A Bambah, M S Sriram and C Mukku,Pramana — J. Phys. 48, 617 (1997)
M S Sriram, inComputational aspects in chaos and nonlinear dynamics edited by G Ambika and V M Nandakumaran (Wiley Eastern, New Delhi, 1994) pp. 37–47
S G Matinyan, E B Prokhorenko, and G K Savvidy,Pis’ma Zh. Eksp. Teor. Fiz. 44, 109 (1986) [JETP Lett. 44, 138 (1986)]
E Fermi, J R Pasta and S M Ulam,Los Alamos Sci. Lab. Tech. Report No. LA-1940 (1955) (unpublished)
M P Joy and M Sabir,J. Phys. A22, 5153 (1989)
M P Joy and M Sabir,Pramana — J. Phys. 38, L91 (1992)
T Kawabe and S Ohta,Phys. Rev. D41, 1983 (1990)
T Kawabe and S Ohta,Phys. Rev. D44,s 1274 (1991)
V G Makhankovet al, in ref [4]Proc. R. Soc. Am. A260, 127 (1961)
J Segar and M S Sriram,Phys. Rev. D53, 3976 (1996)
G Adkins and C Nappi,Nucl. Phys. B233, 109 (1984)
G S Adkins inChiral Solitons edited by K F Liu (World Scientific, Singapore, 1987)
M S Sriram, H S Mani and R Ramachandran,Phys. Rev. D30, 1141 (1984)
E Guadagnini,Nucl. Phys. B236, 35 (1984) see also ref [29]
C G Callan and I Klebanov,Nucl. Phys. B262, 365 (1985)
R L Jaffe,Phys. Rev. Lett. 38, 195 (1977)
J Segar, Baryonic solitons in quark-meson models of strong interaction, Ph.D. Thesis, University of Madras (1994)
M Gellmann and M Levy,Nuovo Cimento 16, 705 (1960)
J A McGovern and M C Birse,Nucl. Phys. A506, 392 (1993)
J Segar and M S Sriram,Pramana — J. Phys. 40, 291 (1993)
M Peyrard, B Piette and W Zakrzewski,Nonlinearity 5, 565, 585 (1992)
A Kudryavtsev, B Piette and W J Zakrzewski,Phys. Lett. A180, 119 (1993)
P Carruthers, E M Friedlander and R M Weiner,Physica D23, 138 (1986)
P Carruthers, E M Friedlander, C C Shih and R M Weiner,Phys. Lett. 222, 487 (1989)
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Sriram, M.S., Segar, J. Nonlinear chiral models: Soliton solutions and spatio-temporal chaos. Pramana - J Phys 48, 205–229 (1997). https://doi.org/10.1007/BF02845631
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DOI: https://doi.org/10.1007/BF02845631