The branch process of cosmic strings

Journal of Mathematical Physics

Volumn 41, Issue 5, 2000, Pages 2616-2628

  Jiang, Ying ^a,b   Duan, Yishi ^c  

^a CCAST WORLD LABORATORY   (China)

^b INSTITUTE OF THEORETICAL PHYSICS   (China)

^c LANZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034347333     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533262     Document Type: Article

References (49)

1. C. Rovelli, "Strings, loops and others: a critical survey of the present approaches to quantum gravity," gr-qc/9803024.
2. M. B. Hindmarsh and T. W. B. Kibble, Rep. Prog. Phys. 58, 477 (1995).
3. A. Vilenkin, Phys. Rep. 121, 263 (1985); M. Robinson and J. Ziabicki, Phys. Rev. D 53, 5924 (1996); I. Bakas, Phys. Lett. B 319, 457 (1993); Int. J. Mod. Phys. A 9, 3443 (1994); I. Bakas and K. Sfetsos, Phys. Rev. D 54, 3995 (1996); A. L. Larsen and N. Sánchez, Phys. Rev. D 54, 2483 (1996); 54, 2801 (1996).
4. A. Vilenkin, Phys. Rep. 121, 263 (1985); M. Robinson and J. Ziabicki, Phys. Rev. D 53, 5924 (1996); I. Bakas, Phys. Lett. B 319, 457 (1993); Int. J. Mod. Phys. A 9, 3443 (1994); I. Bakas and K. Sfetsos, Phys. Rev. D 54, 3995 (1996); A. L. Larsen and N. Sánchez, Phys. Rev. D 54, 2483 (1996); 54, 2801 (1996).
5. A. Vilenkin, Phys. Rep. 121, 263 (1985); M. Robinson and J. Ziabicki, Phys. Rev. D 53, 5924 (1996); I. Bakas, Phys. Lett. B 319, 457 (1993); Int. J. Mod. Phys. A 9, 3443 (1994); I. Bakas and K. Sfetsos, Phys. Rev. D 54, 3995 (1996); A. L. Larsen and N. Sánchez, Phys. Rev. D 54, 2483 (1996); 54, 2801 (1996).
6. A. Vilenkin, Phys. Rep. 121, 263 (1985); M. Robinson and J. Ziabicki, Phys. Rev. D 53, 5924 (1996); I. Bakas, Phys. Lett. B 319, 457 (1993); Int. J. Mod. Phys. A 9, 3443 (1994); I. Bakas and K. Sfetsos, Phys. Rev. D 54, 3995 (1996); A. L. Larsen and N. Sánchez, Phys. Rev. D 54, 2483 (1996); 54, 2801 (1996).
7. A. Vilenkin, Phys. Rep. 121, 263 (1985); M. Robinson and J. Ziabicki, Phys. Rev. D 53, 5924 (1996); I. Bakas, Phys. Lett. B 319, 457 (1993); Int. J. Mod. Phys. A 9, 3443 (1994); I. Bakas and K. Sfetsos, Phys. Rev. D 54, 3995 (1996); A. L. Larsen and N. Sánchez, Phys. Rev. D 54, 2483 (1996); 54, 2801 (1996).
8. A. Vilenkin, Phys. Rep. 121, 263 (1985); M. Robinson and J. Ziabicki, Phys. Rev. D 53, 5924 (1996); I. Bakas, Phys. Lett. B 319, 457 (1993); Int. J. Mod. Phys. A 9, 3443 (1994); I. Bakas and K. Sfetsos, Phys. Rev. D 54, 3995 (1996); A. L. Larsen and N. Sánchez, Phys. Rev. D 54, 2483 (1996); 54, 2801 (1996).
9. A. Vilenkin, Phys. Rep. 121, 263 (1985); M. Robinson and J. Ziabicki, Phys. Rev. D 53, 5924 (1996); I. Bakas, Phys. Lett. B 319, 457 (1993); Int. J. Mod. Phys. A 9, 3443 (1994); I. Bakas and K. Sfetsos, Phys. Rev. D 54, 3995 (1996); A. L. Larsen and N. Sánchez, Phys. Rev. D 54, 2483 (1996); 54, 2801 (1996).
10. A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge U. P., Cambridge, England, 1994).
11. K. A. Meissner and G. Veneziano, Phys. Lett. B 267, 33 (1991); M. Gasperini and G. Veneziano, ibid. 277, 256 (1992).
12. K. A. Meissner and G. Veneziano, Phys. Lett. B 267, 33 (1991); M. Gasperini and G. Veneziano, ibid. 277, 256 (1992).
13. A. de Laix, L. Krauss, and T. Vachaspati, Phys. Rev. Lett. 79, 1968 (1997); A. Achúcarro and R. Gregory, ibid. 79, (1972); M. Galluccio, M. Letterio, and F. Occhionero, ibid. 79, 970 (1997).
14. A. de Laix, L. Krauss, and T. Vachaspati, Phys. Rev. Lett. 79, 1968 (1997); A. Achúcarro and R. Gregory, ibid. 79, (1972); M. Galluccio, M. Letterio, and F. Occhionero, ibid. 79, 970 (1997).
15. A. de Laix, L. Krauss, and T. Vachaspati, Phys. Rev. Lett. 79, 1968 (1997); A. Achúcarro and R. Gregory, ibid. 79, (1972); M. Galluccio, M. Letterio, and F. Occhionero, ibid. 79, 970 (1997).
16. R. Gregory and M. Hindmarsh, Phys. Rev. D 52, 5598 (1995); A. Achúcarro, R. Gregory, and K. Kuijken, Phys. Rev. D 52, 5729 (1995).
17. R. Gregory and M. Hindmarsh, Phys. Rev. D 52, 5598 (1995); A. Achúcarro, R. Gregory, and K. Kuijken, Phys. Rev. D 52, 5729 (1995).
18. Y. S. Duan and Y. Jiang, Int. J. Theor. Phys. 38, 563 (1999).
19. Y. S. Duan and M. L. Ge, Sci. Sin. 11, 1072 (1979); Y. S. Duan and X. H. Meng, J. Math. Phys. 34, 1549 (1993); C. Gu, Phys. Rep. C 80, 251 (1981); Y. S. Duan and X. G. Lee, Helv. Phys. Acta 68, 513 (1995).
20. Y. S. Duan and M. L. Ge, Sci. Sin. 11, 1072 (1979); Y. S. Duan and X. H. Meng, J. Math. Phys. 34, 1549 (1993); C. Gu, Phys. Rep. C 80, 251 (1981); Y. S. Duan and X. G. Lee, Helv. Phys. Acta 68, 513 (1995).
21. Y. S. Duan and M. L. Ge, Sci. Sin. 11, 1072 (1979); Y. S. Duan and X. H. Meng, J. Math. Phys. 34, 1549 (1993); C. Gu, Phys. Rep. C 80, 251 (1981); Y. S. Duan and X. G. Lee, Helv. Phys. Acta 68, 513 (1995).
22. Y. S. Duan and M. L. Ge, Sci. Sin. 11, 1072 (1979); Y. S. Duan and X. H. Meng, J. Math. Phys. 34, 1549 (1993); C. Gu, Phys. Rep. C 80, 251 (1981); Y. S. Duan and X. G. Lee, Helv. Phys. Acta 68, 513 (1995).
23. Y. S. Duan, S. L. Zhang, and S. S. Feng, J. Math. Phys. 35, 1 (1994).
24. Y. S. Duan, S. Li, and G. H. Yang, Nucl. Phys. B 514, 705 (1998).
25. Y. S. Duan and S. L. Zhang, Int. J. Eng. Sci. 28, 689 (1990); 29, 153 (1991); 29, 1593 (1991); 30, 153 (1992);
26. Y. S. Duan and S. L. Zhang, Int. J. Eng. Sci. 28, 689 (1990); 29, 153 (1991); 29, 1593 (1991); 30, 153 (1992); Y. S. Duan and Z. P. Duan, ibid. 24, 531 (1986).
27. Y. S. Duan and S. L. Zhang, Int. J. Eng. Sci. 28, 689 (1990); 29, 153 (1991); 29, 1593 (1991); 30, 153 (1992); Y. S. Duan and Z. P. Duan, ibid. 24, 531 (1986).
28. Y. S. Duan and S. L. Zhang, Int. J. Eng. Sci. 28, 689 (1990); 29, 153 (1991); 29, 1593 (1991); 30, 153 (1992); Y. S. Duan and Z. P. Duan, ibid. 24, 531 (1986).
29. Y. S. Duan and S. L. Zhang, Int. J. Eng. Sci. 28, 689 (1990); 29, 153 (1991); 29, 1593 (1991); 30, 153 (1992); Y. S. Duan and Z. P. Duan, ibid. 24, 531 (1986).
30. Y. S. Duan and S. L. Zhang, Int. J. Eng. Sci. 28, 689 (1990); 29, 153 (1991); 29, 1593 (1991); 30, 153 (1992); Y. S. Duan and Z. P. Duan, ibid. 24, 531 (1986).
31. P. O. Mazur, Phys. Rev. Lett. 57, 929 (1986).
32. V. De Sabbata, Nuovo Cirrento A 107, 363 (1994); V. De Sabbata et al., Int. J. Theor. Phys. 30, 167 (1991).
33. V. De Sabbata, Nuovo Cirrento A 107, 363 (1994); V. De Sabbata et al., Int. J. Theor. Phys. 30, 167 (1991).
34. R. Hammond, Nuovo Cimento B 109, 319 (1994); Gen. Relativ. Gravit. 28, 749 (1996); V. De Sabbata and C. Sivaram, Found. Phys. Lett. 8, 375 (1995).
35. R. Hammond, Nuovo Cimento B 109, 319 (1994); Gen. Relativ. Gravit. 28, 749 (1996); V. De Sabbata and C. Sivaram, Found. Phys. Lett. 8, 375 (1995).
36. R. Hammond, Nuovo Cimento B 109, 319 (1994); Gen. Relativ. Gravit. 28, 749 (1996); V. De Sabbata and C. Sivaram, Found. Phys. Lett. 8, 375 (1995).
37. P. S. Letelier, Class. Quantum Grav. 12, 471 (1995).
38. G. 'tHooft, Nucl. Phys. B 79, 276 (1974).
39. Y. S. Duan, H. Zhang, and L. B. Fu, Phys. Rev. E 59, 528 (1999).
40. J. W. Milnor, Topology, From the Differential Viewpoint (U. P. of Virginia, Charlottesville, 1965); S. Lefschetz, Introduction to Topology (Princeton U. P., Princeton, NJ. 1949); B. A. Dubrovin et al., Modern Geometry Method and Application, Part II (Springer-Verlag, New York, 1985); Y. Choquet-Bruhat et al., Analysis, Manifolds and Physics (North-Holland, Amsterdam, 1977); V. Guillemin and A. Pollack, Differential Topology (Prentice-Hall, Englewood Cliffs, NJ, 1974).
41. J. W. Milnor, Topology, From the Differential Viewpoint (U. P. of Virginia, Charlottesville, 1965); S. Lefschetz, Introduction to Topology (Princeton U. P., Princeton, NJ. 1949); B. A. Dubrovin et al., Modern Geometry Method and Application, Part II (Springer-Verlag, New York, 1985); Y. Choquet-Bruhat et al., Analysis, Manifolds and Physics (North-Holland, Amsterdam, 1977); V. Guillemin and A. Pollack, Differential Topology (Prentice-Hall, Englewood Cliffs, NJ, 1974).
42. J. W. Milnor, Topology, From the Differential Viewpoint (U. P. of Virginia, Charlottesville, 1965); S. Lefschetz, Introduction to Topology (Princeton U. P., Princeton, NJ. 1949); B. A. Dubrovin et al., Modern Geometry Method and Application, Part II (Springer-Verlag, New York, 1985); Y. Choquet-Bruhat et al., Analysis, Manifolds and Physics (North-Holland, Amsterdam, 1977); V. Guillemin and A. Pollack, Differential Topology (Prentice-Hall, Englewood Cliffs, NJ, 1974).
43. J. W. Milnor, Topology, From the Differential Viewpoint (U. P. of Virginia, Charlottesville, 1965); S. Lefschetz, Introduction to Topology (Princeton U. P., Princeton, NJ. 1949); B. A. Dubrovin et al., Modern Geometry Method and Application, Part II (Springer-Verlag, New York, 1985); Y. Choquet-Bruhat et al., Analysis, Manifolds and Physics (North-Holland, Amsterdam, 1977); V. Guillemin and A. Pollack, Differential Topology (Prentice-Hall, Englewood Cliffs, NJ, 1974).
44. J. W. Milnor, Topology, From the Differential Viewpoint (U. P. of Virginia, Charlottesville, 1965); S. Lefschetz, Introduction to Topology (Princeton U. P., Princeton, NJ. 1949); B. A. Dubrovin et al., Modern Geometry Method and Application, Part II (Springer-Verlag, New York, 1985); Y. Choquet-Bruhat et al., Analysis, Manifolds and Physics (North-Holland, Amsterdam, 1977); V. Guillemin and A. Pollack, Differential Topology (Prentice-Hall, Englewood Cliffs, NJ, 1974).
45. I. M. Gel'fand and G. E. Shilov, Generalized Functions (Academic P, New York, 1964), Vol. 1; D. S. Jones, Generalized Functions, (McGraw-Hill, New York, 1966); E. M. De Jager, Mathematics Applied to Physics, edited by E. Roubine, (Springer-Verlag, New York, 1970); J. A. Schouten, Tensor Analysis for Physicists (Clarendon, Oxford, 1951).
46. I. M. Gel'fand and G. E. Shilov, Generalized Functions (Academic P, New York, 1964), Vol. 1; D. S. Jones, Generalized Functions, (McGraw-Hill, New York, 1966); E. M. De Jager, Mathematics Applied to Physics, edited by E. Roubine, (Springer-Verlag, New York, 1970); J. A. Schouten, Tensor Analysis for Physicists (Clarendon, Oxford, 1951).
47. I. M. Gel'fand and G. E. Shilov, Generalized Functions (Academic P, New York, 1964), Vol. 1; D. S. Jones, Generalized Functions, (McGraw-Hill, New York, 1966); E. M. De Jager, Mathematics Applied to Physics, edited by E. Roubine, (Springer-Verlag, New York, 1970); J. A. Schouten, Tensor Analysis for Physicists (Clarendon, Oxford, 1951).
48. I. M. Gel'fand and G. E. Shilov, Generalized Functions (Academic P, New York, 1964), Vol. 1; D. S. Jones, Generalized Functions, (McGraw-Hill, New York, 1966); E. M. De Jager, Mathematics Applied to Physics, edited by E. Roubine, (Springer-Verlag, New York, 1970); J. A. Schouten, Tensor Analysis for Physicists (Clarendon, Oxford, 1951).
49. M. Kubiček and M. Marek, Computational Methods in Bifurcation Theory and Dissipative Structures (Springer-Verlag, New York, 1983).