On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

Nuclear Physics B

Volumn 536, Issue 1-2, 1998, Pages 363-380

  Gattringer, Christof ^a   Hip, Ivan ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF GRAZ   (Austria)

Author keywords

Lattice field theory; Spectrum; Topological charge

Indexed keywords

EID: 0032556614     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00558-6     Document Type: Article

References (66)

1. [1] M. Atiyah and I.M. Singer, Ann. Math. 87 (1968) 596; Ann. Math. 93 (1971) 139.
2. [1] M. Atiyah and I.M. Singer, Ann. Math. 87 (1968) 596; Ann. Math. 93 (1971) 139.
3. [2] P. Colella and O.E. Lanford III, in Constructive Quantum Field Theory (Erice 73), G. Velo and A. Wightman (Eds.), Springer Lecture Notes in Physics, Springer 1973, New York; J. Glimm and A. Jaffe, Quantum Physics (Springer, New York, 1987); A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao and T. Thiemann, in Geometry of Constrained Dynamical Systems Cambridge (1994), hep-th/9408108.
4. [2] P. Colella and O.E. Lanford III, in Constructive Quantum Field Theory (Erice 73), G. Velo and A. Wightman (Eds.), Springer Lecture Notes in Physics, Springer 1973, New York; J. Glimm and A. Jaffe, Quantum Physics (Springer, New York, 1987); A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao and T. Thiemann, in Geometry of Constrained Dynamical Systems Cambridge (1994), hep-th/9408108.
5. [2] P. Colella and O.E. Lanford III, in Constructive Quantum Field Theory (Erice 73), G. Velo and A. Wightman (Eds.), Springer Lecture Notes in Physics, Springer 1973, New York; J. Glimm and A. Jaffe, Quantum Physics (Springer, New York, 1987); A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao and T. Thiemann, in Geometry of Constrained Dynamical Systems Cambridge (1994), hep-th/9408108.
6. [3] B. Alles, M.D. Elia, A. Di Giacomo and R. Kirchner, hep-lat/9711026.
7. [4] F. Karsch, E. Seiler and I.O. Stamatescu, Nucl. Phys. B 271 (1986) 349.
8. [5] J. Smit and J.C. Vink, Nucl. Phys. B 286 (1987) 485.
9. [6] J. Smit and J.C. Vink, Phys. Lett. B 194 (1987) 433; M.L. Laursen, J. Smit and J.C. Vink, Nucl. Phys. B343 (1990) 522.
10. [6] J. Smit and J.C. Vink, Phys. Lett. B 194 (1987) 433; M.L. Laursen, J. Smit and J.C. Vink, Nucl. Phys. B343 (1990) 522.
11. [7] Nucl. Phys. B 284 (1987) 234; B 298 (1988) 557.
12. [7] Nucl. Phys. B 284 (1987) 234; B 298 (1988) 557.
13. [8] J. Smit and J.C. Vink, Nucl. Phys. B 303 (1988) 36; J.C. Vink, Nucl. Phys. B 307 (1988) 549.
14. [8] J. Smit and J.C. Vink, Nucl. Phys. B 303 (1988) 36; J.C. Vink, Nucl. Phys. B 307 (1988) 549.
15. [9] R. Setoodeh, C.T.H. Davies and I.M. Barbour, Phys. Lett. B 213 (1988) 195.
16. [10] S. Itoh, Y. Iwasaki and T. Yoshié, Phys. Rev. D 36 (1987) 527; Phys. Lett. B 184 (1987) 375.
17. [10] S. Itoh, Y. Iwasaki and T. Yoshié, Phys. Rev. D 36 (1987) 527; Phys. Lett. B 184 (1987) 375.
18. [11] R. Narayanan and H. Neuberger, Phys. Rev. Lett. 71 (1993) 3251; Nucl. Phys. B 412 (1994) 574; B 443 (1995) 305.
19. [11] R. Narayanan and H. Neuberger, Phys. Rev. Lett. 71 (1993) 3251; Nucl. Phys. B 412 (1994) 574; B 443 (1995) 305.
20. [11] R. Narayanan and H. Neuberger, Phys. Rev. Lett. 71 (1993) 3251; Nucl. Phys. B 412 (1994) 574; B 443 (1995) 305.
21. [12] R. Narayanan and H. Neuberger, Phys. Lett. B 348 (1995) 549.
22. [13] R. Narayanan, H. Neuberger and P. Vranas, Phys. Lett. B 353 (1995) 507.
23. [14] R. Narayanan and P. Vranas, Nucl. Phys. B 506 (1997) 373.
24. [15] R. Narayanan and R.L. Singleton Jr., Nucl. Phys. B (Proc. Suppl.) 63 (1998) 555; R.G. Edwards, U.M. Heller, R. Narayanan and R.L. Singleton Jr., hep-lat/9711029.
25. [15] R. Narayanan and R.L. Singleton Jr., Nucl. Phys. B (Proc. Suppl.) 63 (1998) 555; R.G. Edwards, U.M. Heller, R. Narayanan and R.L. Singleton Jr., hep-lat/9711029.
26. [16] T. Kalkreuter, Phys. Rev. D 51 (1995) 1305; Nucl. Phys. B (Proc. Suppl.) 49 (1996) 168.
27. [16] T. Kalkreuter, Phys. Rev. D 51 (1995) 1305; Nucl. Phys. B (Proc. Suppl.) 49 (1996) 168.
28. [17] T. Kalkreuter and H. Simma, Comput. Phys. Commun. 95 (1996) 1.
29. [18] M.A. Halasz, T. Kalkreuter and J.J.M. Verbaarschot, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 266; M.E. Berbenni-Bitsch, S. Meyer, A. Schäfer, J.J.M. Verbaarschot and T. Wettig, Phys. Rev. Lett. 80 (1998) 1146.
30. [18] M.A. Halasz, T. Kalkreuter and J.J.M. Verbaarschot, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 266; M.E. Berbenni-Bitsch, S. Meyer, A. Schäfer, J.J.M. Verbaarschot and T. Wettig, Phys. Rev. Lett. 80 (1998) 1146.
31. [19] W, Bardeen, A. Duncan, E. Eichten and H. Thacker, hep-lat/9705002; Phys. Rev. D 57 (1998) 1633.
32. [19] W, Bardeen, A. Duncan, E. Eichten and H. Thacker, hep-lat/9705002; Phys. Rev. D 57 (1998) 1633.
33. [20] J.W. Kegele, hep-lat/9709129; T.L. Ivanenko and J.W. Negele, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 504.
34. [20] J.W. Kegele, hep-lat/9709129; T.L. Ivanenko and J.W. Negele, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 504.
35. [21] J.B. Kogut, J.-F. Lagaë and D.K. Sinclair, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 433.
36. [22] L. Venkataraman and G. Kilcup, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 826.
37. [23] M. García Pérez, A. Gonzalez-Arroyo, A. Montero and C. Pena, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 501.
38. [24] C.R. Gattringer, I. Hip and C.B. Lang, Nucl. Phys. B 508 (1997) 329; Nucl. Phys. B (Proc. Suppl.) 63 (1998) 498.
39. [24] C.R. Gattringer, I. Hip and C.B. Lang, Nucl. Phys. B 508 (1997) 329; Nucl. Phys. B (Proc. Suppl.) 63 (1998) 498.
40. [25] K. Jansen, C. Liu, H. Simma and D. Smith, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 262; D. Smith, H. Simma and M. Teper, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 558.
41. [25] K. Jansen, C. Liu, H. Simma and D. Smith, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 262; D. Smith, H. Simma and M. Teper, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 558.
42. [26] I. Montvay and G. Münster, Quantum Fields on a Lattice (Cambridge Univ. Press, Cambridge, 1994).
43. [27] D.H. Weingarten and J.L. Challifour, Ann. Phys. 123 (1979) 61.
44. [28] M. Lüscher, Commun. Math. Phys. 85 (1982) 39.
45. [29] A. Phillips and D. Stone, Commun. Math. Phys. 103 (1986) 599.
46. [30] I. Fox, J. Gilchrist, J. Laursen and G. Schierholz, Phys. Rev. Lett. 54 (1985) 749.
47. [31] P. de Forcrand, M. García Pérez and I.-O. Stamatescu, Nucl. Phys. B499 (1997) 409; P. de Forcrand, M. García Pérez, J,E. Hetrick and I.O. Stamatescu, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 549.
48. [31] P. de Forcrand, M. García Pérez and I.-O. Stamatescu, Nucl. Phys. B499 (1997) 409; P. de Forcrand, M. García Pérez, J,E. Hetrick and I.O. Stamatescu, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 549.
49. [32] T. DeGrand, A. Hasenfratz and T. Kovacs, Nucl. Phys. B 505 (1997) 417; Nucl. Phys. B (Proc. Suppl.) 63 (1998) 528; hep-lat/9711032.
50. [32] T. DeGrand, A. Hasenfratz and T. Kovacs, Nucl. Phys. B 505 (1997) 417; Nucl. Phys. B (Proc. Suppl.) 63 (1998) 528; hep-lat/9711032.
51. [33] C.R. Gattringer, I. Hip and C.B. Lang, Phys. Lett. B 409 (1997) 371.
52. [34] J.K. Cullum and R.A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1, Theory (Birkhäuser, Boston, 1985).
53. [35] I. Barbour, E. Laermann, Th. Lippert and K. Schilling, Phys. Rev. D 46 (1992) 3618.
54. [36] K.G. Wilson, in New Phenomena in Subnuclear Physics (Erice 75) ed. A. Zichichi (Plenum, New York, 1977).
55. [37] R. Flume and D. Wyler, Phys. Lett. B 108 (1981) 317; C. Panagiotakopoulos, Nucl. Phys. B 251 (1985) 61; A. Phillips, Ann. Phys. 161 (1985) 399; M. Göckeler, A.S. Kronfeld, G. Schierholz and U.-J. Wiese, Nucl. Phys. B 404 (1993) 839; H. Gausterer and M. Sammer, hep-lat/9609032.
56. [37] R. Flume and D. Wyler, Phys. Lett. B 108 (1981) 317; C. Panagiotakopoulos, Nucl. Phys. B 251 (1985) 61; A. Phillips, Ann. Phys. 161 (1985) 399; M. Göckeler, A.S. Kronfeld, G. Schierholz and U.-J. Wiese, Nucl. Phys. B 404 (1993) 839; H. Gausterer and M. Sammer, hep-lat/9609032.
57. [37] R. Flume and D. Wyler, Phys. Lett. B 108 (1981) 317; C. Panagiotakopoulos, Nucl. Phys. B 251 (1985) 61; A. Phillips, Ann. Phys. 161 (1985) 399; M. Göckeler, A.S. Kronfeld, G. Schierholz and U.-J. Wiese, Nucl. Phys. B 404 (1993) 839; H. Gausterer and M. Sammer, hep-lat/9609032.
58. [37] R. Flume and D. Wyler, Phys. Lett. B 108 (1981) 317; C. Panagiotakopoulos, Nucl. Phys. B 251 (1985) 61; A. Phillips, Ann. Phys. 161 (1985) 399; M. Göckeler, A.S. Kronfeld, G. Schierholz and U.-J. Wiese, Nucl. Phys. B 404 (1993) 839; H. Gausterer and M. Sammer, hep-lat/9609032.
59. [37] R. Flume and D. Wyler, Phys. Lett. B 108 (1981) 317; C. Panagiotakopoulos, Nucl. Phys. B 251 (1985) 61; A. Phillips, Ann. Phys. 161 (1985) 399; M. Göckeler, A.S. Kronfeld, G. Schierholz and U.-J. Wiese, Nucl. Phys. B 404 (1993) 839; H. Gausterer and M. Sammer, hep-lat/9609032.
60. [38] J. Kiskis, Phys. Rev. D 15 (1977) 2329; N.K. Nielsen and B. Schroer, Nucl. Phys. B 127 (1977) 493; M.M. Ansourian, Phys. Lett. B 70 (1977) 301.
61. [38] J. Kiskis, Phys. Rev. D 15 (1977) 2329; N.K. Nielsen and B. Schroer, Nucl. Phys. B 127 (1977) 493; M.M. Ansourian, Phys. Lett. B 70 (1977) 301.
62. [38] J. Kiskis, Phys. Rev. D 15 (1977) 2329; N.K. Nielsen and B. Schroer, Nucl. Phys. B 127 (1977) 493; M.M. Ansourian, Phys. Lett. B 70 (1977) 301.
63. [39] R.G. Edwards, U.M. Heller and R. Narayanan, hep-lat/9801015; hep-lat/9802016.
64. [40] H. Simma and D. Smith, hep-lat/9801025.
65. [41] P. Hernandez, hep-lat/9801035.
66. [42] F. Farchioni and V. Laliena, hep-lat/9802009.