Quantum evolution across singularities: the case of geometrical resolutions

Understand

We continue the study of time-dependent Hamiltonians with an isolated singularity in their time dependence, describing propagation on singular space-times.

• In previous work, two of us have proposed a "minimal subtraction" prescription for the simplest class of such systems, involving Hamiltonians with only one singular term.
• On the other hand, Hamiltonians corresponding to geometrical resolutions of space-time tend to involve multiple operator structures (multiple types of dependence on the canonical variables) in an essential way.
• We consider some of the general properties of such (near-)singular Hamiltonian systems, and further specialize to the case of a free scalar field on a two-parameter generalization of the null-brane space-time.