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## Banach Center Publications

1997 | 39 | 1 | 389-403
Tytuł artykułu

### An axiomatic approach to Quantum Gauge Field Theory

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connections modulo gauge transformations rather than for the associated Schwinger distributions. We show non-triviality of our axioms by demonstrating that they are satisfied for two-dimensional Yang-Mills theory on the plane and the cylinder. As a side result we derive a closed and analytical expression for the vacuum expectation value of an arbitrary product of Wilson-loop functionals from which we derive the quantum theory along the Glimm and Jaffe algorithm which agrees exactly with the one as obtained by canonical methods.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
389-403
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
• Physics Department, Harvard University Cambridge, MA 02138, U.S.A.
Bibliografia
• [1] A. Ashtekar, New Hamiltonian formulation of general relativity, Phys. Rev. D 36 (1987), 1587-1602.
• [2] A. Ashtekar, C. J. Isham, Representation of the holonomy algebras of gravity and nonabelian gauge theories, Classical Quantum Gravity 9 (1992), 1433-1467.
• [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.
• [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.
• [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.
• [6] J. Baez, Spin network states in gauge theory, Adv. Math. (in press).
• [7] M. Creutz, Quarks, Gluons and Lattices, Cambridge University Press, New York, 1983.
• [8] R. Giles, Reconstruction of gauge potentials from Wilson loops, Phys. Rev. D 24 (1981), 2160-2168.
• [9] J. Glimm, A. Jaffe, Quantum Physics, 2nd ed., Springer, New York, 1987.
• [10] L. Gross, C. King, A. Sengupta, Two-dimensional Yang-Mills theory via stochastic differential equations, Ann. Physics 194 (1989), 65-112.
• [11] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, San Diego, 1978.
• [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] S. Klimek, W. Kondracki, A construction of two-dimensional quantum chromodynamics, Comm. Math. Phys. 113 (1987), 389-402.
• [14] D. Marolf, J. M. Mourão, On the support of the Ashtekar-Lewandowski measure, Comm. Math. Phys. 170 (1995), 583-606.
• [15] V. Rivasseau, From perturbative to constructive renormalization, Princeton University Press, Princeton, 1991.
• [16] C. Rovelli, L. Smolin, Spin-networks and quantum gravity, Preprint CGPG-95/4-4.
• [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] T. Thiemann, A Minlos theorem for gauge theories, in preparation.
• [19] T. Thiemann, The inverse loop transform, Preprint CGPG-95/7-1.
• [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] T. T. Wu, C. N. Yang, Some remarks about unquantized non-abelian gauge fields, Phys. Rev. D 12 (1975), 3843-3844.
• [22] Y. Yamasaki, Measures on infinite dimensional spaces, World Scientific, Philadelphia, 1985.
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Bibliografia
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