On the Gribov problem for generalized connections

Communications in Mathematical Physics

Volumn 234, Issue 3, 2003, Pages 423-454

  Fleischhack, Christian ^a,b  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037359517     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0745-9     Document Type: Article

References (45)

1. Ashtekar, A., Isham, C.J.: Representations of the holonomy algebras of gravity and nonabelian gauge theories. Class. Quant. Grav. 9, 1433-1468 (1992)
2. Ashtekar, A., Lewandowski, J.: Representation theory of analytic holonomy C* algebras. In: Knots and Quantum Gravity. J.C. Baez (ed.). Proceedings, Riverside, CA, 1993, Oxford: Oxford University Press, 1994, pp. 21-61
3. Ashtekar, A., Lewandowski, J.: Projective techniques and functional integration for gauge theories. J. Math. Phys. 36, 2170-2191 (1995)
4. Ashtekar, A., Lewandowski, J.: Relation between polymer and Fock excitations. Class. Quant. Grav. 18, L117-L128 (2001)
5. Ashtekar, A., Lewandowski, J., Marolf, D., Mourão, J., Thiemann, T.: SU (N) quantum Yang-Mills theory in two dimensions: A complete solution. J. Math. Phys. 38, 5453-5482 (1997)
6. Ashtekar, A., Marolf, D., Mourão, J., Thiemann, T.: Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism-invarianl context. Class. Quant. Grav. 17, 4919-4940 (2000)
7. Asorey, M., Falceto, F., López, J.L., Luzón, G.: Nodes, monopoles and confinement in (2 + 1)-dimensional gauge theories. Phys. Lett. B349, 125-130 (1995)
8. Baez. J.C., Sawin, S.: Functional integration on spaces of connections. J. Funct. Anal. 150, 1-26 (1997)
9. Baum, M., Friedrich, T.: A group-theoretical study of the stabilizer of a generic connection. Ann. Glob. Anal. Geom. 3, 120-128 (1985)
10. Bredon, G.E.: Introduction to Compact Transformation Groups. New York: Academic Press, Inc., 1972
11. Bröcker, Th., tom Dieck, T.: Representations of Compact Lie Groups. New York: Springer, 1985
12. Daniel, M., Viallet, C.M.: The gauge fixing problem around classical solutions of the Yang-Mills theory. Phys. Lett. B76, 458-460 (1978)
13. Dell'Antonio, G., Zwanziger, D.: Ellipsoidal bound on the Gribov horizon contradicts the perturbative renormalization group. Nucl. Phys. B326, 333-350 (1989)
14. Dell'Antonio, G., Zwanziger, D.: Every gauge orbit passes inside the Gribov horizon. Commun. Math. Phys. 138, 291-299 (1991)
15. Dieudonné, J.: Grundzüge der modernen Analysis, Bd. 3. Berlin: VEB Deutscher Verlag der Wissenschaften, 1976
16. Dieudonné, J.: Grundzüge der modernen Analysis, Bd. 4. Berlin: VEB Deutscher Verlag der Wissenschaften, 1976
17. Emmrich, C., Römer. H.: Orbifolds as configuration spaces of systems with gauge symmetries. Commun. Math. Phys. 129, 69-94 (1990)
18. Faddeev, L.D., Popov, V.N.: Feynman diagrams for the Yang-Mills field. Phys. Lett. B25, 29-30 (1967)
19. Fleischhack, Ch.: On the support of physical measures in gauge theories, e-print: math-ph/0109030
20. Fleischhack, Ch.: Regular connections among generalized connections. To appear in J. Geom. Phys.
21. Fleischhack, Ch.: A new type of loop independence and SU (N) quantum Yang-Mills theory in two dimensions. J. Math. Phys. 41, 76-102 (2000)
22. Fleischhack, Ch.: Hyphs and the Ashtekar-Lewandowski measure. J. Geom. Phys. (to appear)
23. Fleischhack, Ch.: Stratification of the generalized gauge orbit space. Commun. Math. Phys. 214, 607-649(2000)
24. Fleischhack, Ch.: Mathematische und physikalische Aspekte verallgemeinerter Eichfeldtheorien im Ashtekarprogramm (Dissertation). Universität Leipzig, 2001
25. Fuchs, J., Schmidt, M.G., Schweigert, Ch.: On the configuration space of gauge theories. Nucl. Phys. B426, 107-128 (1994)
26. Glimm, J., Jaffe, A.: Quantum Physics: A Functional Integral Point of View. New York: Springer, 1987
27. Gribov, V.N.: Quantization of non-abelian gauge theories. Nucl. Phys. B139, 1-19 (1978)
28. Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. San Diego: Academic Press, Inc., 1978
29. Hilgert, J., Neeb, K.-H.: Lie-Gruppen and Lie-Algebren. Braunschweig/Wiesbaden: Friedr. Vieweg & Sohn, 1991
30. Husemoller, D.: Fibre Bundles. New York: Springer, 1994
31. Kelley, J.L.: General Topology. Toronto, New York, London: D. van Nostrand Company, Inc., 1955
32. Kondracki, W., Rogulski, J.: On the stratification of the orbit space for the action of automorphisms on connections. Dissertationes mathematicae 250, Warszawa:- 1985
33. Kondracki, W., Sadowski, P.: Geometric structure on the orbit space of gauge connections. J. Geom. Phys. 3, 421-434 (1986)
34. Kurosch, A.G.: Gruppentheorie 1. Berlin: Akademie-Verlag, 1970
35. McMullan, D.: Constrained quantisation, gauge fixing and the Gribov ambiguity. Commun. Math. Phys. 160, 431-456 (1994)
36. 1979. Extended Russian translation of the English original edition: Milnor, J.W., Stasheff, J.D.: Characteristic Classes. Princeton: Princeton University Press, 1974
37. Mitter, P.K.: Geometry of the space of gauge orbits and the Yang-Mills dynamical system. Lectures given at Cargèse Summer Inst. on Recent Developments in Gauge Theories, Cargèse, France, Aug 26-Sep 8, 1979
38. Mitter, P.K., Viallet, C.M.: On the bundle of connections and the gauge orbit manifold in Yang-Mills theory. Commun. Math. Phys. 79, 457-472 (1981)
39. Onishchik, A.L. (ed.): Lie Groups and Lie Algebras I (Encyclopaedia of Mathematical Sciences 20). Berlin: Springer-Verlag, 1993
40. Singer, I.M.: Some Remarks on the Gribov ambiguity. Commun. Math. Phys. 60, 7-12 (1978)
41. van Baal, P.: More (thoughts on) Gribov copies. Nucl. Phys. B369, 259-275 (1992)
42. 1-complexes. Annal. Math. 41, 809-824 (1940)
43. Whitney, H.: Geometric Integration Theory. Princeton, NJ: Princeton University Press, 1957
44. Yabuki, H.: Structure of the Gribov horizon for the non-abelian gauge field theory in axial gauges. Phys. Lett. B231, 271-274 (1989)
45. Zwanziger, D.: Fundamental modular domain, Boltzmann factor and area law in lattice theory. Nucl. Phys. B412, 657-730 (1994)