Low-order Hamiltonian operators having momentum

The Spectra of Operators Having Resolvents of First-order Growth^)

Oscillatory Integral Operators with Low–order Degeneracies

We prove sharp L estimates for oscillatory integral and Fourier integral operators for which the associated canonical relation C ⊂ T ∗ΩL × T ∗ΩR projects to T ∗ΩL and to T ∗ΩR with corank one singularities of type ≤ 2. This includes two-sided cusp singularities. Applications are given to operators with one-sided swallowtail singularities such as restricted X-ray transforms for well-curved line ...

Momentum operators on graphs

We discuss ways in which momentum operators can be introduced on an oriented metric graph. A necessary condition appears to the balanced property, or a matching between the numbers of incoming and outgoing edges; we show that a graph without an orientation, locally finite and at most countably infinite, can made balanced oriented iff the degree of each vertex is even. On such graphs we construc...

Hamiltonian and Volume Operators

2+1 gravity coupled to a massless scalar field has an initial singularity when the spatial slices are compact. The quantized model is used here to investigate several issues of quantum gravity. The spectrum of the volume operator is studied at the initial singularity. The energy spectrum is obtained. Dynamics of the universe is also investigated.

Hamiltonian Monte Carlo with Reduced Momentum Flips

Hamiltonian dynamics with partial momentum refreshment, in the style of [Horowitz, 1991], explore the state space more slowly than they otherwise would due to the momentum reversals which occur on proposal rejection. These cause trajectories to double back on themselves, leading to random walk behavior on timescales longer than the typical rejection time, and leading to slower mixing. I present...