An axiomatic approach to Quantum Gauge Field Theory

 Access to full text

 Full (PDF)

1. [1] A. Ashtekar, New Hamiltonian formulation of general relativity, Phys. Rev. D 36 (1987), 1587-1602. 
2. [2] A. Ashtekar, C. J. Isham, Representation of the holonomy algebras of gravity and nonabelian gauge theories, Classical Quantum Gravity 9 (1992), 1433-1467. Zbl0773.53033
3. [3] A. Ashtekar, J. Lewandowski, Representation Theory of analytic holonomy $C^{*}$ algebras, in: Knots and quantum gravity, J. Baez (ed.), Oxford University Press, 1994, 21-61. Zbl0827.46055
4. [4] A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, T. Thiemann, A manifestly gauge invariant approach to quantum theories of gauge fields, in: Geometry of Constrained Dynamical Systems, J. Charap (ed.), Cambridge University Press, Cambridge, 1994, 60-86. Zbl0834.58044
5. [5] A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, T. Thiemann, Euclidean Yang-Mills Theory in two dimensions: A complete solution, Preprint CGPG-95/7-3. Zbl0891.53058
6. [6] J. Baez, Spin network states in gauge theory, Adv. Math. (in press). Zbl0843.58012
7. [7] M. Creutz, Quarks, Gluons and Lattices, Cambridge University Press, New York, 1983. 
8. [8] R. Giles, Reconstruction of gauge potentials from Wilson loops, Phys. Rev. D 24 (1981), 2160-2168. 
9. [9] J. Glimm, A. Jaffe, Quantum Physics, 2nd ed., Springer, New York, 1987. Zbl0461.46051
10. [10] L. Gross, C. King, A. Sengupta, Two-dimensional Yang-Mills theory via stochastic differential equations, Ann. Physics 194 (1989), 65-112. Zbl0698.60047
11. [11] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, San Diego, 1978. Zbl0451.53038
12. [12] V. A. Kazakov, Wilson loop average for an arbitrary contour in two-dimensional U(N) gauge theory, Nuclear Phys. B 179 (1981), 283-292. 
13. [13] S. Klimek, W. Kondracki, A construction of two-dimensional quantum chromodynamics, Comm. Math. Phys. 113 (1987), 389-402. Zbl0629.58037
14. [14] D. Marolf, J. M. Mourão, On the support of the Ashtekar-Lewandowski measure, Comm. Math. Phys. 170 (1995), 583-606. Zbl0846.58065
15. [15] V. Rivasseau, From perturbative to constructive renormalization, Princeton University Press, Princeton, 1991. 
16. [16] C. Rovelli, L. Smolin, Spin-networks and quantum gravity, Preprint CGPG-95/4-4. 
17. [17] E. Seiler, Gauge theories as a problem of constructive quantum field theory and statistical mechanics, Lecture Notes in Phys. 159, Springer, Berlin, 1982. 
18. [18] T. Thiemann, A Minlos theorem for gauge theories, in preparation. 
19. [19] T. Thiemann, The inverse loop transform, Preprint CGPG-95/7-1. Zbl0912.58008
20. [20] T. T. Wu, C. N. Yang, Concept of nonintegrable phase factors and global formulation of gauge fields, Phys. Rev. D 12 (1975), 3845-3857. 
21. [21] T. T. Wu, C. N. Yang, Some remarks about unquantized non-abelian gauge fields, Phys. Rev. D 12 (1975), 3843-3844. 
22. [22] Y. Yamasaki, Measures on infinite dimensional spaces, World Scientific, Philadelphia, 1985.