Branched Quantization
arXiv:1207.2677 · doi:10.1103/PhysRevLett.109.200402
Abstract
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.
5 pages, 2 figures. v2: Eqn.(20) corrected, minor typos fixed
References in corpus (3)
Cited by in corpus (23)
- Quantum Time Crystals
- Time crystals: a review
- Classical Time Crystals
- Colloquium: Quantum and Classical Discrete Time Crystals
- Quantum Oppenheimer-Snyder model
- formalism in Einstein-scalar-Gauss-Bonnet gravity
- Consistent Quantization of Nearly Singular Superconducting Circuits
- Suppressing Quantum Fluctuations in Classicalization
- Oscillatory Attractors: A New Cosmological Phase
- From classical to quantum Oppenheimer-Snyder model: non-marginal case
- Models of Topology Change
- One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form
- Geometrical description and Faddeev-Jackiw quantization of electrical networks
- Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity
- Canonical structure of higher derivative theories
- Time Crystals in the Driven Transverse Field Ising Model under Quasiperiodic Modulation
- Branched Hamiltonians and Supersymmetry
- Exploring Branched Hamiltonians for a Class of Nonlinear Systems
- The issue of Branched Hamiltonian in F(T) Teleparallel Gravity
- A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians
- Branched Hamiltonians for a class of Velocity Dependent Potentials
- One-parameter supersymmetric Hamiltonians in momentum space
- The Inertial Spin Model of flocking with position-dependent forces