Bundle gerbes applied to quantum field theory

Reviews in Mathematical Physics

Volumn 12, Issue 1, 2000, Pages 65-90

  Carey, Alan L ^a   Mickelsson, Jouko ^b   Murray, Michael K ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034390017     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X00000046     Document Type: Article

References (34)

1. M. F. Atiyah and I. M. Singer, "Dirac operators coupled to vector potentials", Natl. Acad. Sci. (USA) 81 (1984) 2597.
2. M. F. Atiyah, V. K. Patodi and I. M. Singer, "Spectral asymmetry and Riemannian Geometry", I-III. Math. Proc. Camb. Phil. Soc. 77 (1975) 43; 78 (1975) 405; 79 (1976) 71.
3. M. F. Atiyah, V. K. Patodi and I. M. Singer, "Spectral asymmetry and Riemannian Geometry", I-III. Math. Proc. Camb. Phil. Soc. 77 (1975) 43; 78 (1975) 405; 79 (1976) 71.
4. M. F. Atiyah, V. K. Patodi and I. M. Singer, "Spectral asymmetry and Riemannian Geometry", I-III. Math. Proc. Camb. Phil. Soc. 77 (1975) 43; 78 (1975) 405; 79 (1976) 71.
5. E. J. Beggs, "The de Rham complex on infinite dimensional manifolds." Quart. J. Math. Oxford 38(2) (1987) 131-154.
6. J.-L. Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Birkhäuser, Boston-Basel-Berlin, 1993.
7. A. L. Carey, D. Crowley and M. K. Murray, "Principal bundles and the Dixmier Douady class", Commun. Math. Phys. 193 (1998) 171-196, hep-th/9702147.
8. A. L. Carey, J. Mickelsson and M. K. Murray, "Index theory, gerbes and Hamiltonian quantization", Commun. Math. Phys., 183 (1997) 707-722.
9. A. L. Carey, J. Mickelsson and M. K. Murray, Bundle Gerbes and Field Theory, Proc. Int. Congress of Math. Phys. Brisbane, 1997.
10. A. L. Carey and M. K. Murray, Confronting the Infinite, Proc. Conference in Celebration of the 70th Years of H. S. Green and C. A. Hurst, World Scientific, 1995, hep-th/9408141.
11. A. L. Carey and M. K. Murray, "Faddeev's anomaly and bundle gerbes", Letts. in Math. Phys. 37 (1996) 29-36.
12. A. L. Carey and M. K. Murray, "Holonomy and the Wess-Zumino term", Letts. in Math. Phys. 12 (1986) 323-328.
13. A. L. Carey, M. K. Murray and B. Wang, "Higher bundle gerbes, descent equations and 3-Cocycles", to appear in J. Geometry and Phys., hep-th/9511169.
14. J. Dixmier and A. Douady, "Champs continus d'espaces hilbertiens et de C* algebres", Bull. Soc. Math. Fr. 91 (1963) 227.
15. S. K. Donaldson and P. B. Kronheimer, The Geometry of Four-Manifolds, Clarendon Press, Oxford, 1990.
16. S. Elitzur and V. P. Nair, "Nonperturbative anomalies in higher dimensions", Nucl. Phys. B243 (1984) 205.
17. L. Faddeev and S. Shatasvili, "Algebraic and Hamiltonian methods in the theory of nonabelian anomalies", Theoret. Math. Phys. 60 (1985) 770.
18. K. Gawedski, "Topological actions in two-dimensional quantum field theories", in Nonperturbative Quantum Field Theory, eds. G. 't Hooft et al., Cargese, 1987, 101-141, NATO Adv. Sci. Inst. Ser. B: Phys ., 185, New York, Plenum Press, 1988.
19. K. Gawedski, "Topological actions in two-dimensional quantum field theories", in Nonperturbative Quantum Field Theory, eds. G. 't Hooft et al., Cargese, 1987, 101-141, NATO Adv. Sci. Inst. Ser. B: Phys ., 185, New York, Plenum Press, 1988.
20. T. Killingback, "World sheet anomalies and loop geometry", Nucl. Phys. B288 (1987) 578-588.
21. D. A. McLaughlin, "Orientation and string structures on loop space", Pac. J. Math. 155 (1992) 1-31.
22. J. Mickelsson, "Chiral anomalies in even and odd dimensions", Commun. Math. Phys. 97 (1985) 361.
23. J. Mickelsson, "On the Hamiltonian approach to commutator anomalies in 3 + 1 dimensions", Phys. Lett. B241 (1990) 70.
24. J. Mickelsson, Current Algebras and Groups, Plenum Press, London, New York, 1989.
25. J. Mickelsson, "Hilbert space cocycles as representations of (3 + 1) - D current algebras", Lett. Math. Phys. 28 (1993) 97.
26. J. Milnor, "On infinite dimensional Lie groups", preprint.
27. M. K. Murray, "Bundle gerbes", J. London Math. Soc. 54(2) (1996), 403-416, dg-ga/9407015.
28. M. K. Murray and D. Stevenson, "Bundle gerbes: Stable isomorphism and classifying theory", math.DG/9908135.
29. P. Nelson and L. Alvarez-Gaume, "Hamiltonian interpretation of anomalies", Commun. Math. Phys. 99 (1985) 103.
30. A. Pressley and G. Segal, Loop Groups, Clarendon Press, Oxford, 1986.
31. G. Segal, "Faddeev's anomaly in Gauss's law", preprint.
32. D. Stevenson, "Bundle gerbes", PhD thesis in preparation.
33. E. Witten, An SU(2) anomaly, Phys. Lett. 117B (1982) 324.
34. E. Witten, "Current algebra, baryons, and quark confinement" Nucl. Phys. B223 (1983) 433.