Branched Quantization

Understand

We propose a method for quantization of Lagrangians for which the Hamiltonian, as a function of momentum, is a branched function with cusps.

• Appropriate boundary conditions, which we identify, insure unitary time evolution.
• In special cases a dual (canonical) transformation maps the problem into a problem of quantum mechanics on singular spatial manifolds, which we also develop.
• Several possible applications are indicated.