Nonperturbative weak-coupling analysis of the quantum Liouville field theory |
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Authors: | E Braaten T Curtright G Ghandour C Thorn |
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Affiliation: | Physics Department, University of Florida, Gainesville, Florida 32611 USA |
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Abstract: | Two independent weak-coupling expansions are developed for the Liouville quantum field theory on a circle. In the first, the coupling of the nonzero modes is treated as a perturbation on the exact solution to the zero-mode problem (quantum mechanics with an exponential potential). The second approach is a weak-coupling approximation to an explicit operator solution which expresses various Liouville operators as functions of a free massless field using a Bäcklund transformation. It is shown that the free state space associated with the latter solution must be restricted to the sector which is odd with respect to a type of “parity.” Various matrix elements are computed to order g10 using both approaches, yielding identical results. |
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