Operator Approach to Boundary Liouville Theory

Understand

We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature.

• They are based on the structure of the vertex operator $V=e^{-\phi}$ in terms of the asymptotic operators.
• The methods first are tested for the particle dynamics in the Morse potential, where similar structures appear.
• Application of our methods to boundary Liouville theory reproduces the known results obtained earlier in the bootstrap approach, but there can arise a certain extension when the boundary parameters are near to critical values.