Prog. Theor. Phys. Vol. 89 No. 2 (1993) pp. 501-522

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How to Solve the Covariant Operator Formalism of Gauge Theories and Quantum Gravity in the Heisenberg Picture. III

— Two-Dimensional Nonabelian BF Theory —

Mitsuo Abe and Noboru Nakanishi

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01

(Received September 10, 1992)

Abstract:

The two-dimensional nonabelian BF theory is studied, which turns out to be essentially the zeroth-order approximation to QCD in the framework of the newly proposed method of solving quantum field theory in the Heisenberg picture. The exact covariant operator solution and some lower-point exact Wightman functions are constructed explicitly. It is shown that there is no ultraviolet divergence in the Wightman functions. In the context of the BF theory, the system coupled with the Dirac field is also studied.

URL : http://ptp.ipap.jp/link?PTP/89/501/
DOI : 10.1143/PTP.89.501

References:

M. Abe and N. Nakanishi, Prog. Theor. Phys. 88 (1992), 975[PTP].
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K. Sato, Preprint EPHOU87 APR003 (Hokkaido, 1987).
M. Abe and N. Nakanishi, Int. J. Mod. Phys. A6 (1991), 3955.
M. Abe and N. Nakanishi, Prog. Theor. Phys. 86 (1991), 517[PTP].
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Citing Article(s) :

Progress of Theoretical Physics Vol. 90 No. 3 (1993) pp. 705-716 :
How to Solve the Covariant Operator Formalism of Gauge Theories and Quantum Gravity in the Heisenberg Picture. IV

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Progress of Theoretical Physics Vol. 90 No. 4 (1993) pp. 911-916 :
Another Perturbative Expansion in Nonabelian Gauge Theory

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Progress of Theoretical Physics Vol. 90 No. 5 (1993) pp. 1091-1109 :
New Diagrammatic Method for Quantum Field Theory in the Heisenberg Picture. I

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Progress of Theoretical Physics Vol. 90 No. 6 (1993) pp. 1319-1342 :
New Diagrammatic Method for Quantum Field Theory in the Heisenberg Picture. II

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Progress of Theoretical Physics Vol. 100 No. 5 (1998) pp. 1063-1075 :
Anomaly Problem in a Simple Model Analogous to the Lightcone-Gauge Two-Dimensional Quantum Gravity

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Progress of Theoretical Physics Vol. 102 No. 6 (1999) pp. 1187-1200 :
Perturbative or Path-Integral Approach versus Operator-Formalism Approach

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Progress of Theoretical Physics Vol. 111 No. 3 (2004) pp. 301-337 :
Method for Solving Quantum Field Theory in the Heisenberg Picture

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