Precanonical quantization of Yang-Mills fields, and the functional Schrödinge representation

Reports on Mathematical Physics

Volumn 53, Issue 2, 2004, Pages 181-193

  Kanatchikov, Igor V ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Clifford algebra; De Donder Weyl formalism; Functional Schr dinger representation; Magnetic opreator; Mass gap; Precanonical quantization; Yang Mills theory

Indexed keywords

EID: 2942719052     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(04)90011-0     Document Type: Article

References (36)

1. M. J. Gotay, J. Isenberg and J. Marsden: Momentum maps and classical relativistic fields, Part I: Covariant field theory, physics/9801019 (and the references therein).
2. I. V. Kanatchikov: Rep. Math. Phys. 41 (1998), 49-90; hep-th/9709229.
3. I. V. Kanatchikov: Rep. Math. Phys. 40 (1997), 225-234; hep-th/9710069.
4. M. Forger, C. Paufler and H. Römer: Rev. Math. Phys. 15 (2003), No. 7; hep-th/0202043.
5. A. Echeverría-Enríquez, M. C. Muñoz-Lecanda and N. Roman-Roy: J. Math. Phys. 41 (2000), 7402-7444; math-ph/0004005.
6. G. Giachetta, L. Mangiarotti and G. Sardanashvily: New Lagrangian and Hamiltonian Methods in Field Theory, World Scientific, Singapore 1997.
7. L. K. Norris: J. Math. Phys. 42 (2001), 4827-4845.
8. M. de León, M. McLean, L. K. Norris, A. Rey-Roca and M. Salgado: Geometric structures in field theory, math-ph/0208036 (and the references therein).
9. F. Hélein, J. Kouneiher: Covariant Hamiltonian formalism for the calculus of variations with several variables, math-ph/0211046.
10. Th. De Donder: Théorie Invariantive du Calcul des Variations, Gauthier-Villars, Paris (1935);
11. H. Weyl: Ann. Math. (2) 36 (1935), 607-629
12. H. Rund: The Hamilton-Jacobi Theory in the Calculus of Variations, D. van Nostrand, Toronto 1966.
13. I. V. Kanatchikov: Int. J. Theor. Phys. 37 (1998), 333-342; quant-ph/9712058.
14. I. V. Kanatchikov: Rep. Math. Phys. 43 (1999), 157-170; hep-th/9810165.
15. I. V. Kanatchikov: in: Particles, Fields and Gravitation (Proc. Int. Conf. Łódź, Poland, Apr. 1998) J. Rembielinski (ed.), AIP Conf. Proc. vol. 453, p. 356-367, Amer. Inst. Phys., Woodbury (NY) 1998; hep-th/9811016.
16. I. V. Kanatchikov: Int. J. Theor. Phys. 40 (2001), 1121-1149; gr-qc/0012074.
17. I. V. Kanatchikov: Geometric (pre)quantization in the polysymplectic approach to field theory; hep-th/0112263.
18. I. V. Kanatchikov: Phys. Lett. A283 (2001), 25-36; hep-th/0301001.
19. W. Kondracki: Rep. Math. Phys. 16 (1979), 9-47;
20. J. Kijowski and G. Rudolph: Rep. Math. Phys. 20 (1984), 385-400.
21. M. C. López and J. E. Marsden: J. Geom. Phys. 48 (2003), 52-83.
22. R. P. Feynman: Nucl. Phys. B188 (1981), 479-512.
23. B. F. Hatfield: Phys. Lett. 154B (1985), 296-302.
24. M. Lüscher, R. Narayanan, P. Weisz and U. Wolff: Nucl. Phys. B384 (1992), 168-228.
25. G. C. Rossiand M. Testa: Nucl. Phys. B163 (1980), 109;
26. ibid. B176 (1980), 477;
27. ibid. B237 (1984), 442.
28. B. Hatfield: Quantum Field Theory of Point Particles and Strings, Reading MA: Addison-Wesley 1992.
29. P. Mansfield and M. Sampaio: Nucl. Phys. B545 (1999), 623-655; hep-th/9807163.
30. J. D. Dollard and C. N. Friedman: Product Integration, Reading MA: Addison-Wesley 1979.
31. B. Simon: Ann. Phys. 146 (1983), 209-220.
32. I. V. Kanatchikov, work in progress.
33. A. Gonzalez-Lopez and N. Kamran: J. Geom. Phys. 26 (1998), 202-226; hep-th/9612100.
34. P. A. M. Dirac: Proc. Roy. Soc. (London) A133 (1931), 60-72.
35. J. Avron, I. Herbst and B. Simon: Duke Math. J. 45 (1978), 847-883;
36. V. Kondrat'ev and M. Shubin: Comm. Part. Diff. Eqs. 27 (2002), 477-525, math.SP/0007111.