Zero Mode Problem of Liouville Field Theory

Details Zero Mode Problem of Liouville Field Theory Zero Mode Problem of Liouville Field Theory

2002-07-04

arxiv.org/abs/hep-th/0207041v2

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, latex, 4 figures, chap. 3.2 extended, chap. 3.3 new, former chap. 3.3 as App. E

Scientific paper

We quantise canonical free-field zero modes $p$, $q$ on a half-plane $p>0$ both, for the Liouville field theory and its reduced Liouville particle dynamics. We describe the particle dynamics in detail, calculate one-point functions of particle vertex operators, deduce their zero mode realisation on the half-plane, and prove that the particle vertex operators act self-adjointly on a Hilbert space $L^2(\rr_+)$ on account of symmetries generated by the $S$-matrix. Similarly, self-adjointness of the corresponding vertex operator of Liouville field theory in the zero mode sector is obtained by applying the Liouville reflection amplitude, which is derived by the operator method.

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