Perturbation theory with a variational basis: The generalized Gaussian effective potential

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 55, Issue 8, 1997, Pages 4967-4989

  Cea, Paolo ^a   Tedesco, Luigi ^a  

^a INFN SEZIONE DI BARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001495892     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.55.4967     Document Type: Article

References (59)

1. P. M. Stevenson, Phys. Rev. D30, 1712 (1984);
2. 32, 1389 (1985).
3. For a review, see E. Feenberg, Theory of Quantum Fluids (Academic, New York, 1969);
4. J.W. Clark, in The Many-Body Problem, edited by R. Guardiola and J. Ros, Lecture Notes in Physics Vol. 138 (Springer, Berlin, 1981);
5. J.W. Clark and E. Krotscheck, in Recent Progress in Many-Body Physics, edited by H. Kümmel and M. L. Ristig, Lecture Notes in Physics Vol. 198 (Springer, Berlin, 1983).
6. L. I. Schiff, Phys. Rev.130, 458 (1963);
7. G. Rosen, 173, 1632 (1968).
8. J. M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D10, 2428 (1974).
9. T. Barnes and G. I. Ghandour, Phys. Rev. D22, 924 (1980).
10. S. Colemann and E. Weinberg, Phys. Rev. D7, 1888 (1973);
11. S. Weinberg, 7, 2887 (1973);
12. R. Jackiw, 9, 1686 (1973).
13. G. Jona-Lasinio, Nuovo Cimento 34, 1790 (1964);
14. K. Symanzik, Commun. Math. Phys.16, 48 (1970);
15. S. Coleman, in Law of Hadronic Matter, edited by A. Zichichi (Academic Press, New York, 1975).
16. P. Cea, Phys. Lett. B236, 191 (1990).
17. A wider discussion can be found in P. Cea, Phys. Rev. D37, 1637 (1988).
18. K. A. Brueckner, Phys. Rev.100, 36 (1955);
19. J. Goldstone, Proc. R. Soc. LondonA239, 267 (1957).
20. For a clear exposition, see A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle System (McGraw-Hill, New York, 1971).
21. M. Gell-Mann and F. Low, Phys. Rev.84, 350 (1951).
22. P. Cea and L. Tedesco, Phys. Lett. B335, 423 (1994).
23. For a lucid discussion, see R. P. Feynman, in Variational Calculation in Quantum Field Theory, edited by L. Polley and D. E. L. Pottingen (World Scientific, Singapore, 1988).
24. S. J. Chang, Phys. Rev. D12, 1071 (1975);
25. Phys. Rep. C23, 301 (1975).
26. S. J. Chang, Phys. Rev. D13, 2778 (1976).
27. B. Simon and R. G. Griffiths, Commun. Math. Phys.33, 145 (1975).
28. See, for instance, P. Ramond, Field Theory a Modern Primer (Addison-Wesley, New York, 1990).
29. L. Polley and U. Ritschel, Phys. Lett. B221, 2778 (1989).
30. M. H. Thoma, Z. Phys. C44, 343 (1989).ZPCFD2
31. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1980).
32. I. Stancu and P. M. Stevenson, Phys. Rev. D42, 2710 (1990).
33. I. Stancu, Phys. Rev. D43, 1283 (1991).
34. A. Peter, J. M. Häuser, M. H. Thoma, and W. Cassing, Z. Phys. C71, 515 (1996).ZPCFD2
35. F. S. Magruder, Phys. Rev. D14, 1602 (1976).
36. S. Chang and F. S. Magruder, Phys. Rev. D16, 983 (1977).
37. C. W. Bernard, Phys. Rev. D9, 3312 (1974).
38. S. Weinberg, Phys. Rev. D9, 3357 (1974).
39. L. Dolan and R. Jackiw, Phys. Rev. D9, 3320 (1974).
40. G. A. Hajj and P. M. Stevenson, Phys. Rev. D37, 413 (1988).
41. I. Roditi, Phys. Lett.169B, 264 (1986);
42. B. Alles and R. Tarrach, Phys. Rev. D33, 1718 (1986);
43. 34, 664 (1986);
44. A. Bardeen and M. Moshe, 34, 1229 (1986);
45. A. Okopinska, 35, 1835 (1987);
46. 36, 2415 (1987).
47. T. Matsubara, Prog. Theor. Phys.14, 351 (1955).
48. See, for instance, R. Feynman, Statistical Mechanics (Benjamin, New York, 1982).
49. P. Cea and L. Tedesco, “Finite Temperature Generalized Gaussian Effective Potential, ” Report No. Bari-Th 198/95 (unpublished).
50. See, for instance, A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinki, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1975).
51. E. K. U. Gross, E. Runge, and O. Heinonen, Many-Particle Theory (Adam Hilger, Bristol, 1991).
52. M. B. Kislinger and P. D. Morley, Phys. Rev. D13, 2779 (1976).
53. P. Cea and L. Tedesco, “Generalized Gaussian Effective Potential: Second Order Thermal Corrections, ” Report No. Bari-Th 208/95 (unpublished).
54. H. W. L. Naus, T. Gasenzer, and H. J. Pirner, “Effective Hamiltonian for Scalar Theories in the Gaussian Approximation,”Report No.(unpublished).
55. R. Fernandez, J. Fröhlich, and A. D. Sokal, Random Walks, Critical Phenomena, and Quantum Field Theory (Springer-Verlag, Berlin, 1992).
56. M. Consoli and P. M. Stevenson, Z. Phys. C63, 427 (1994).ZPCFD2
57. A. Agodi, G. Adronico, and M. Consoli, Z. Phys. C66, 439 (1995).ZPCFD2
58. P. Cea, L. Cosmai, M. Consoli, and R. Fiore, “Lattice effective potential of (Formula presented): nature of the phase transition and bounds on the Higgs mass,”Report No.(unpublished).
59. A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1967).