Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-03-29
Phys.Rev. D48 (1993) 1736-1747
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, KANAZAWA 93-2
Scientific paper
10.1103/PhysRevD.48.1736
Two-dimensional quantum gravity is identified as a second-class system which we convert into a first-class system via the Batalin-Fradkin (BF) procedure. Using the extended phase space method, we then formulate the theory in most general class of gauges. The conformal gauge action suggested by David, Distler and Kawai is derived from a first principle. We find a local, light-cone gauge action whose Becchi-Rouet-Stora-Tyutin invariance implies Polyakov's curvature equation $\partial_{-}R=\partial_{-}^{3}g_{++}=0$, revealing the origin of the $SL(2,R)$ Kac-Moody symmetry. The BF degree of freedom turns out be dynamically active as the Liouville mode in the conformal gauge, while in the light-cone gauge the conformal degree of freedom plays that r{\^o}le. The inclusion of the cosmological constant term in both gauges and the harmonic gauge-fixing are also considered.
Fujiwara Takanori
Igarashi Yuji
Kubo Jisuke
Tabei Takao
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