title: Branched quantization.
abstract: We propose a method for quantization of Lagrangians for which the Hamiltonian, as a function of momentum, is a branched function, possibly with cusps. Appropriate boundary conditions, which we identify, ensure unitary time evolution. In special cases a dual (canonical) transformation maps the problem into a problem of quantum mechanics on singular spaces, which we also develop. Several possible applications are indicated.
authors.affiliation: Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.
authors.forename: Alfred
authors.initials: A
authors.lastname: Shapere
authors.forename: Frank
authors.initials: F
authors.lastname: Wilczek