We discuss elementary entwiners that cross-weave the variables of certain integrable models: Liouville, sine-Gordon, and sinh-Gordon field theories in two-dimensional spacetime, and their quantum mechanical reductions. First we define a complex time parameter that varies from one energy-shell to another. Then we explain how field propagators can be simply expressed in terms of elementary functi...

We compute the sphere and disk partition functions in semiclassical Liouville analogous quantities double-scaled matrix integrals. The quantity sphere/disk^2 is unambiguous we find a precise numerical match between answer integral answer. An application to show that function JT gravity infinite.

We develop a level set method for the computation of multivalued physical observables (density, velocity, etc.) for the semiclassical limit of the Schrödinger equation. This method uses an Eulerian formulation and applies directly to arbitrary number of space dimensions. The main idea is to evolve the density near an n-dimensional manifold that is identified as the common zeros of n level set f...