A New Type of Conformal Dynamics

Abstract

We consider the Lagrangian particle model introduced in [hep-th/9612017] for zero mass but nonvanishing second central charge of the planar Galilei group. Extended by a magnetic vortex or a Coulomb potential the model exibits conformal symmetry. In the former case we observe an additional SO(2,1) hidden symmetry. By either a canonical transformation with constraints or by freezing scale and special conformal transformations at $t=0$ we reduce the six-dimensional phase-space to the physically required four dimensions. Then we discuss bound states (bounded solutions) in quantum dynamics (classical mechanics). We show that the Schrödinger equation for the pure vortex case may be transformed into the Morse potential problem thus providing us with an explanation of the hidden SO(2,1) symmetry.

24 pages

References in corpus (4)

• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• Noncommutative Planar Particle Dynamics with Gauge Interactions
• Galilean symmetry in noncommutative field theory

Cited by in corpus (16)

• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
• Comments on Galilean conformal field theories and their geometric realization
• Schrodinger Equations for Higher Order Non-relativistic Particles and N-Galilean Conformal Symmetry
• Galilean Superconformal Symmetries
• Galilean Conformal Mechanics from Nonlinear Realizations
• Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations
• On irreducible representations of the exotic conformal Galilei algebra
• Ricci-flat spacetimes with l-conformal Galilei symmetry
• N = 2 Galilean superconformal algebras with central extension
• Acceleration-extended Newton-Hooke symmetry and its dynamical realization
• Galilean conformal algebras in two spatial dimension
• Lowest weight representations of super Schrodinger algebras in low dimensional spacetime
• Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras
• Supersymmetry in the Non-Commutative Plane
• Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension