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liouville_theory [2021/06/29 22:25]
Brian McPeak [Lagrangian Picture] 		liouville_theory [2021/06/29 22:36] (current)
Brian McPeak [Bootstrap Picture]
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 ===Some Remaining questions=== ===Some Remaining questions===
-  * This theory has no ground state. So how do I normalize the partition function?+  * How is the partition function normalized in a theory with no ground state?
  
 =====Lagrangian Picture===== =====Lagrangian Picture=====
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 This is equivalent to Liouville's equation, which is the source of the theory's name.  This is equivalent to Liouville's equation, which is the source of the theory's name. 
 +
 +It is instructive to consider the wavefunction of states which ``scatter" off the potential barrier $V(\phi)$. This takes the form
 +
 +\begin{align}
 +  \Psi_P(\phi) \sim e^{2 i P \phi} + R(P) e^{-2 i P \phi}
 +\end{align}
 +
 +Here $R(P)$ is the reflection amplitude for incoming plane-waves with momentum $P$, and may be computed from the equation of motion. The wave functions $\Psi$ describe the states which map to the Virarsoro primaries of Liouville theory under the state-operator correspondence. 
  
 =====External Links===== =====External Links=====
Last modified: 2021/06/29 22:25
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