Variational worldline approximation for the relativistic two-body bound state in a scalar model

Few-Body Systems

Volumn 39, Issue 3-4, 2006, Pages 193-253

  Barro Bergflodt K ^a   Rosenfelder, R ^b   Stingl, M ^c  

^a ETH ZURICH   (Switzerland)

^b PAUL SCHERRER INSTITUTE   (Switzerland)

^c UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748573338     PISSN: 01777963     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00601-006-0160-4     Document Type: Article

References (123)

1. Salpeter, E. E., Bethe, H. A.: Phys. Rev. 84, 1232 (1951)
2. Nakanishi, N. (ed.): Progr. Theor. Phys. Suppl. 95 (1988)
3. Sauli, V., Adam, J.: Phys. Rev. D67, 085007 (2003) [arXiv:hep-ph/0111433]
4. Karmanov, V. A., Carbonell, J.: [arXiv:nucl-th/0510051]; [arXiv:hep-th/0505262]
5. Logunov, A. A., Tavkhelidze, A. N.: Nuovo Cim. 29, 380 (1963)
6. Blankenbecler, R., Sugar, R.: Phys. Rev. 142, 1051 (1966)
7. Gross, F.: Phys. Rev. 186,1448 (1969);
8. Phys. Rev. D10, 223 (1974);
9. Phys. Rev. C26, 2203 (1982)
10. Mangin-Brinet, M., Carbonell, J., Karmanov, V. A.: Phys. Rev. C68, 055203 (2003) [arXiv:hep-th/03081791;
11. Bernard, D., Cousin, T., Karmanov, V. A., Mathiot, J. F.: Phys. Rev. D65, 025016 (2002) [arXiv:hep-th/0109208];
12. Mangin-Brinet, M., Carbonell, J., Karmanov, V. A.: Phys. Rev. D64, 125005 (2001) [arXiv:hep-th/0107235];
13. Sales, J. H. O., Frederico, T., Carlson, B. V., Sauer, P. U.: Phys. Rev. C61, 044003 (2000) [arXiv:nucl-th/9909029];
14. Phys. Rev. C63, 064003 (2001);
15. Carbonell, J., Desplanques, B., Karmanov, V. A., Mathiot, J. F.: Phys. Rept. 300, 215 (1998) [arXiv:nucl-th/9804029J;
16. Brodsky, S. J., Pauli, H. C., Pinsky, S. S.: Phys. Rept. 301, 299 (1998) [arXiv:hep-ph/9705477]
17. Desplanques, B.: Nucl. Phys. A748, 139 (2005) [arXiv:nucl-th/04050591;
18. Desplanques, B., Theußl, L.: Eur. Phys. J. A13, 461 (2002) [arXiv:nucl-th/0102060];
19. Klink, W. H.: Phys. Rev. C58, 3587 (1998)
20. Şavkli, Ç., Gross, F., Tjon, J.: Phys. Atom. Nucl. 68, 842 (2005)
21. [Yad. Fiz. 68, 874 (2005)], [arXiv:nucl-th/0404068];
22. Simonov, Y. A., Tjon, J. A.: Ann. Phys. (NY) 300, 54 (2002) [arXiv:hep-ph/0205165];
23. Şjavkli, Ç: Comput. Phys. Commun. 135, 312 (2001) [arXiv:hep-ph/9910502];
24. Şavkh, Ç., Tjon, J., Gross, F.: Phys. Rev. C60,055210 (1999) [arXiv:hep-ph/9906211]; [Erratum: Phys. Rev. C61, 069901 (2000)]
25. Eides, M. I., Grotch, H., Shelyuto, V. A.: Phys. Rept. 342, 63 (2001) [arXiv:hep-ph/0002158];
26. Kinoshita, T. (ed.): Quantum Electrodynamics. Singapore: World Scientific 1990
27. Gilman, R., Gross, F.: J. Phys. G28, R37 (2002) [arXiv:nucl-th/0111015];
28. Gross, F.: Eur. Phys. J. A17, 407 (2003) [arXiv:nucl-th/0209088]
29. Phillips, D. R., Wallace, S. J., Devine, N. K.: Phys. Rev. C58, 2261 (1998) [arXiv:nucl-th/9802067]
30. Montvay, I., Münster, G.: Quantum Fields on a Lattice. Cambridge: Cambridge University Press 1994
31. Alkover, R., von Smekal, L.: Phys. Rept. 353, 281 (2001) [arXiv:hep-ph/0007355]
32. Maris, P., Roberts, C. D.: Int. J. Mod. Phys. E12, 297 (2003) [arXiv:nucl-th/0301049];
33. Roberts, C. D., Schmidt, S. M.: Prog. Part. Nucl. Phys. 45, S1 (2000) [arXiv:nucl-th/0005064]
34. Brambilla, N., Pineda, A., Soto, J., Vairo, A.: Rev. Mod. Phys. 77, 1423 (2005) [arXiv:hep-ph/0410047]
35. Polley, L., Pottinger, D. E. L. (eds.): Variational Calculations in Quantum Field Theory. Singapore: World Scientific 1988
36. Darewych, J. W., Terekidi, A. G.: J. Math. Phys. 46, 032302 (2005) [arXiv:hep-ph/0311132]; Terekidi, A. G., Darewych, J. W.: [arXiv:hep-th/0303250] ;
37. Darewych, J. W., Shpytko, V.: Phys. Rev. D64, 045012 (2001) [arXiv:nucl-th/0012080]
38. Darewych, J. W., Ding, B.: Nucl. Phys. Proc. Suppl. 90, 136 (2000);
39. Ding, B., Darewych, J. W.: J. Phys. G26, 907 (2000) [arXiv:nucl-th/ 9908022];
40. Darewych, J. W.: Can. J. Phys. 76, 523 (1998) [arXiv:nucl-th/9807006];
41. Darewych, J. W., Barham, M.: J. Phys. A31, 3481 (1998);
42. Darewych, J. W., Shapoval, D. V., Simoneg, I. V., Sitenko, A. G.: J. Math. Phys. 38, 3908 (1997);
43. Darewych, J. W., Polozov, A. D., Di Leo, L.: J. Phys. G21, 1167 (1995)
44. Feynman, R. P.: Phys. Rev. 97, 660 (1955)
45. Mano, K.: Prog. Theor. Phys. 14, 435 (1955)
46. Strassler, M. J.: Nucl. Phys. B385, 145 (1992) [arXiv:hep-ph/9205205];
47. Reuter, M., Schmidt, M. G., Schubert, C.: Ann. Phys. (NY) 259, 313 (1997) [arXiv:hep-th/9610191];
48. Schubert, C.: Phys. Rept. 355, 73 (2001) [arXiv:hep-th/0101036]
49. Rosenfelder, R., Schreiber, A. W.: Phys. Rev. D53, 3337 (1996) [arXiv:nucl-th/9504002], denoted by [I] in the text
50. Rosenfelder, R., Schreiber, A. W.: Phys. Rev. D53, 3354 (1996) [arXiv:nucl-th/9504005], denoted by [II] in the text
51. Schreiber, A. W., Rosenfelder, R., Alexandrou, C.: Int. J. Mod. Phys. E5, 681 (1996) [arXiv:nucl-th/95040231
52. Schreiber, A. W., Rosenfelder, R.: Nucl. Phys. A601, 397 (1996) [arXiv:nucl-th/9510032]
53. Alexandrou, C., Rosenfelder, R., Schreiber, A. W.: Nucl. Phys. A628, 427 (1998) [arXiv:nucl-th/97010361;
54. Fettes, N., Rosenfelder, R.: Few-Body Systems 24, 1 (1998)
55. Rosenfelder, R., Schreiber, A. W.: Eur. Phys. J. C25, 139 (2002) [arXiv:hep-th/0112212]
56. Wick, G. C.: Phys. Rev. 96, 1124 (1954);
57. Cutkosky, R. E.: Phys. Rev. 96, 1135 (1954)
58. Alexandrou, C., Rosenfelder, R., Schreiber, A. W.: Phys. Rev. A59, 1762 (1999) [arXiv:hep-th/9809101]
59. Rosenfelder, R., Schreiber, A. W.: Eur. Phys. J. C37, 161 (2004) [arXiv:hep-th/0406062]
60. Baym, G.: Phys. Rev. 117, 886 (1960); Rosenfelder, R., Schreiber, A. W.: [arXiv:hep-ph/99114841;
61. Gross, F., Şavkli, Ç., Tjon, J.: Phys. Rev. D64,076008 (2001) [arXiv:nucl-th/0102041]
62. Alexandrou, C., Rosenfelder, R., Schreiber, A. W.: Phys. Rev. D62, 085009 (2000) [arXiv:hep-th/0003253]
63. Itzykson, C., Zuber, J.-B.: Quantum Field Theory. New York: McGraw-Hill 1980
64. Barro-Bergflödt, K., Rosenfelder, R., Stingl, M.: Mod. Phys. Lett. A20,2533 (2005) [arXiv:hep-ph/040330]
65. Verbist, G., Peeters, F. M., Devreese, J. T.: Phys. Rev. B43, 2712 (1991);
66. Adamowski, J.: Phys. Rev. B39, 3649 (1989)
67. Verbist, G., Smondyrev, M. A., Peeters, F. M., Devreese, J. T.: Phys. Rev. B45, 5262 (1992)
68. Poliatzky, N.: J. Phys. A25, 3649 (1992); see Eq. (37) and Table 1
69. Fetter, A. L., Walecka, J. D.: Quantum Theory of Many-Particle Systems. New York: McGraw-Hill 1971
70. Shifman, M. A., Vainshtein, A. I., Zakharov, V. I.: Nucl. Phys. B147, 385, 448, 519 (1979)
71. Abramowitz, M., Stegun, I. (eds.): Handbook of Mathematical Functions. New York: Dover 1965
72. Ynduráin, F. J.: Quantum Chromodynamics. An Introduction to the Theory of Quarks and Gluons. Berlin Heidelberg New York: Springer 1983
73. Thirring, W.: Quantum Mathematical Physics (2nd Ed.), p. 527. Berlin Heidelberg New York: Springer 2002;
74. Robinett, R. W.: Quantum Mechanics, p. 421. Oxford: Oxford University Press 1997
75. Baye, D., Heenen, P.-H.: J. Phys. A19, 2041 (1986);
76. Semay, C., Baye, D., Hesse, M., Silvestre-Brac, B.: Phys. Rev. E64, 016703 (2001);
77. Buisseret, F., Semay, C.: Phys. Rev. E71, 026705 (2005) [arXiv:hep-ph/04090331
78. Ahlig, S., Alkofer, R.: Ann. Phys. (NY) 275, 113 (1999)
79. Affleck, I. K., De Luccia, F.: Phys. Rev. D20, 3168 (1979);
80. Voloshin, M.: Phys. Rev. D49, 2014 (1994);
81. Calzetta, E., Roura, A., Verdaguer, E.: Phys. Rev. D64, 105008 (2001) [arXiv:hep-ph/0106091]; Gorsky, A., Voloshin, M. B.: [arXiv:hep-th/0511095]
82. Eflmov, G. V.: Few-Body Systems 33, 199 (2003) [arXiv:hep-ph/0304194]
83. Nieuwenhuis, T., Tjon, J. A.: Few-Body Systems 21, 167 (1996) [arXiv:nucl-th/9607041]
84. Karmanov, V. A., Carbonell, J.: Eur. Phys. J. A27, 1 (2006) [arXiv:hep-th/0505261]
85. Efimov, G. V.: Private communication (February 2004)
86. Nieuwenhuis, T., Tjon, J. A.: Phys. Rev. Lett. 77, 814 (1996) [arXiv:hep-ph/9606403]
87. Caswell, W. E., Lepage, G. P.: Phys. Lett. B167, 437 (1986);
88. Pineda, A., Soto, J.: Phys. Rev. D59, 016005 (1999) [arXiv:hep-ph/ 9805424]
89. Grießhammer, H. W.: Phys. Rev. D58, 094027 (1998) [arXiv:hep-ph/9712467]
90. Ji, C. R.: Phys. Lett. B322, 389 (1994)
91. Mathiot, J. F., Karmanov, V. A., Smirnov, A.: Few-Body Systems 36, 173 (2005) [arXiv:hep-th/0412199]
92. Pilkuhn, H. M.: Relativistic Quantum Mechanics. Berlin Heidelberg New York: Springer 2003
93. Todorov, I. T.: Phys. Rev. D3, 2351 (1971)
94. Brezin, E., Itzykson, C., Zinn-Justin, J.: Phys. Rev. D1, 2349 (1970)
95. Jentschura, U. D.: Phys. Lett. B564, 225 (2003) [arXiv:hep-ph/0305072];
96. Jentschura, U. D., Mohr, P. J., Soff, G.: Phys. Rev. Lett. 82, 53 (1999) [arXiv:physics/0001068]
97. Marshall, J. T., Mills, L. R.: Phys. Rev. B2, 3143 (1970);
98. Rosenfelder, R., Lu, Y.: Phys. Rev. B46, 5211 (1992)
99. Luttinger, J. M., Lu, C.-Y.: Phys. Rev. B21, 4251 (1980);
100. Rosenfelder, R.: J. Phys. A27, 3523 (1994)
101. Alexandrou, C., Diakonos, F. K.: Z. Phys. A353, 149 (1995) [arXiv:nucl-th/9503010]
102. Rosenfelder, R.: [arXiv:hep-ph/0601088]
103. D'Hoker, E., Gagne, D. G.: Nucl. Phys. B467, 297 (1996) [arXiv:hep-th/9512080]
104. Kondo, K.-I.: [arXiv:hep-th/0307270, hep-th/0311033]
105. Rosenfelder, R.: (to be published)
106. Binosi, D., Theußl, L.: Comput. Phys. Commun. 161, 76 (2004) [arXiv:hep-ph/0309015]
107. Ericson, T., Weise, W.: Pions and Nuclei. Oxford: Clarendon Press 1988
108. Efimov, G. V.: [arXiv:hep-ph/9907483]; [arXiv:hep-ph/9607425]
109. Bèg, M. A. B., Furlong, R. C.: Phys. Rev. D31, 1370 (1985)
110. Lighthill, M. J.: Introduction to Fourier Analysis and Generalized Functions. Cambridge: Cambridge University Press 1958
111. Robinson, P. A.: J. Math. Phys. 27, 1206 (1986);
112. J. Math. Phys. 30, 2484 (1989)
113. Agrest, M. M., Maksimov, M. S.: Theory of Incomplete Cylindrical Functions and Their Application (Die Grundlehren der mathematischen Wissenschaften, Band 160). Berlin Heidelberg New York: Springer 1971
114. Hauck, A., von Smekal, L., Alkofer, R.: Comput. Phys. Commun. 112, 166 (1998) [arXiv:hep-ph/9804376]
115. Maas, A.: [arXiv:hep-ph/0504110]
116. Mandelzweig, V. B.: Phys. Atom. Nucl. 68, 1227 (2005)
117. [Yad. Fiz. 68, 1277 (2005)]
118. Pineda, A., Soto, J.: Nucl. Phys. Proc. Suppl. 64, 428 (1998) [arXiv:hep-ph/9707481];
119. Phys. Rev. D59, 016005 (1999) [arXiv:hep-ph/9805424]
120. Antonelli, A., Gall, A., Gasser, J., Rusetsky, A.: Ann. Phys. (NY) 286, 108 (2001) [arXiv:hep-ph/0003118]
121. Muta, T.: Foundations of Quantum Chromodynamics. An Introduction to Perturbative Methods in Gauge Theories, Chapt. 2.3.2. Singapore: World Scientific 1987
122. Gall, A.: [arXiv:hep-ph/9910364]
123. Manohar, A. V.: Phys. Rev. D56, 230 (1997) [arXiv:hep-ph/9701294]