Categorified symplectic geometry and the classical string

Communications in Mathematical Physics

Volumn 293, Issue 3, 2009, Pages 701-725

  Baez, John C ^a   Hoffnung, Alexander E ^a   Rogers, Christopher L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 71249086281     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-009-0951-9     Document Type: Article

References (37)

1. Aschieri P., Cantini L., Jurčo B.: Nonabelian bundle gerbes, their differential geometry and gauge theory. Commun. Math. Phys. 254, 367-400 (2005).
2. Aschieri P., Jurčo B.: Gerbes, M5-brane anomalies and E8 gauge theory. J. High Energy Phys. 10, 068 (2004).
3. Baez J.: Higher-dimensional algebra II: 2-Hilbert spaces. Adv. Math. 127, 125-189 (1997).
4. Baez, J., Baratin, A., Freidel, L., Wise, D.: Representations of 2-groups on higher Hilbert spaces. http://arxiv.org/abs/0812.4969v1, 2008.
5. Baez J., Crans A.: Higher-dimensional algebra VI: Lie 2-algebras. Theory Appl. Categ. 12, 492-528 (2004).
6. Baez J., Crans A., Stevenson D., Schreiber U.: From loop groups to 2-groups. Homology, Homotopy Appl. 9, 101-135 (2007).
7. Baez J., Lauda A.: Higher-dimensional algebra V: 2-groups. Theory Appl. Categ. 12, 423-491 (2004).
8. Baez, J., Schreiber, U.: Higher gauge theory. In: Davydov, A. et al (eds.) Categories in Algebra, Geometry and Mathematical Physics. Contemp. Math. 431, Providence, RI: Amer. Math. Soc., 2007, pp. 7-30.
9. Bartels, T.: Higher gauge theory: 2-bundles. http://arxiv.org/abs/math/0410328v3, 2006.
10. Breen L., Messing W.: Differential geometry of gerbes. Adv. Math. 198, 732-846 (2005).
11. Brylinski J.-L.: Loop Spaces, Characteristic Classes and Geometric Quantization. Birkhauser, Boston (1993).
12. Cantrijn F., Ibort A., De Leon M.: On the geometry of multisymplectic manifolds. J. Austral. Math. Soc. Ser. A 66, 303-330 (1999).
13. Cartin, D.: Generalized symplectic manifolds. http://arxiv.org/abs/dg-ga/9710027v2, 1997.
14. Cariñena J. F., Crampin M., Ibort L. A.: On the multisymplectic formalism for first order field theories. Diff. Geom. Appl. 1, 345-374 (1991).
15. DeDonder T.: Theorie Invariantive du Calcul des Variations. Gauthier-Villars, Paris (1935).
16. Diaconescu, E., Moore, G., Freed, D.: The M-theory 3-form and E8 gauge theory. In: Miller, H. R., Ravenel D. C. (eds.), Elliptic Cohomology. London Math. Soc. Lecture Note Ser. 342, Cambridge: Cambridge Univ. Press, 2007, pp. 44-88.
17. Freed D.: Higher algebraic structures and quantization. Commun. Math. Phys. 159, 343-398 (1994).
18. Freed D.: Dirac charge quantization and generalized differential cohomology. In: Yau, S.-T. (eds) Surveys in Differential Geometry VII, pp. 129-194. International Press, Somerville, MA (2000).
19. Freed D., Witten E.: Anomalies in string theory with D-branes. Asian J. Math. 3, 819-851 (1999).
20. Gotay, M., Isenberg, J., Marsden, J., Montgomery, R.: Momentum maps and classical relativistic fields. Part I: covariant field theory. http://arxiv.org/abs/physics/9801019v2, 2004.
21. Guillemin V., Sternberg S.: Symplectic Techniques in Physics. Cambridge U. Press, Cambridge (1984).
22. Hélein, F.: Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory. In: Bahri, A. et al, eds., Noncompact Problems at the Intersection of Geometry, Providence, RI: Amer. Math. Soc., 2001, pp. 127-148.
23. Hélein F., Kouneiher J.: The notion of observable in the covariant Hamiltonian formalism for the calculus of variations with several variables. Adv. Theor. Math. Phys. 8, 735-777 (2004).
24. Ibort, A.: Multisymplectic geometry: generic and exceptional. In: Grácia, X. et al, eds. Proceedings of the IX Fall Workshop on Geometry and Physics, Vilanova i la Geltrú, 2000. Publicaciones de la RSME 3, Madrid: Real Sociedad Matemática Española, 2001, pp. 79-88.
25. Kanatchikov I.: Canonical structure of classical field theory in the polymomentum phase space. Rep. Math. Phys. 41, 49-90 (1998).
26. Kalb M., Ramond P.: Classical direct interstring action. Phys. Rev. D 9, 2273-2284 (1974).
27. Kijowski J.: A finite-dimensional canonical formalism in the classical field theory. Commun. Math. Phys. 30, 99-128 (1973).
28. Lada T., Stasheff J.: Introduction to sh Lie algebras for physicists. Int. J. Theor. Phys. 32, 1087-1103 (1993).
29. Rovelli, C.: Covariant Hamiltonian formalism for field theory: Hamilton-Jacobi equation on the space G. http://arxiv.org/abs/gr-qc/0207043v2, 2002.
30. Roytenberg, D.: On weak Lie 2-algebras. In: Kielanowski, P. et al, eds, XXVI Workshop on Geometrical Methods in Physics. AIP Conference Proceedings 956, Melville: American Institute of Physics, 2007, pp. 180-198.
31. Saunders, D. J.: The Geometry of Jet Bundles. London Math. Soc. Lecture Note Ser. 142, Cambridge: Cambridge U. Press, 1989.
32. ∞-algebra connections and applications to String- and Chern- Simons n-transport. http://arxiv.org/abs/0801.3480v2, 2008.
33. Sati, H., Schreiber, U., Stasheff, J.: Fivebrane structures. http://arxiv.org/abs/0805.0564v3, 2009.
34. Schreiber, U.: From Loop Space Mechanics to Nonabelian Strings. Ph. D. thesis, Universität Duisburg-Essen (2005); http://arxiv.org/abs/hep-th/0509163v1, 2005.
35. Weyl H.: Geodesic fields in the calculus of variation for multiple integrals. Ann. Math. 36, 607-629 (1935).
36. Yetter D.: Measurable categories. Appl. Cat. Str. 13, 469-500 (2005).
37. Zunger, Y.: p-Gerbes and extended objects in string theory. http://arxiv.org/abs/hep-th/0002074v2, 2000.