On the geometry of conformal mechanics

A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the singularity related to the phenomenon of "falling on the center" is spurious. This opens new possibilities concerning both the interpretation and quantization of the model. Moreover, similar modification seem to be relevant in supersymmetric and multidimensional generalization of conformal mechanics.Comment: 8 pages, 4 figures, two references adde

N-Galilean conformal algebras and higher derivatives Lagrangians

It is shown that the N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the free Lagrangian involving (N+1)/2-th order time derivative

Unitary representations of N-conformal Galilei group

All unitary irreducible representations of centrally extended (N-odd) N-conformal Galilei group are constructed. The "on-shell" action of the group is derived and shown to coincide, in special but most important case, with that obtained in: J. Gomis, K. Kamimura, Phys. Rev. {\bf D85} (2012), 045023.Comment: References update

Nonrelativistic conformal groups and their dynamical realizations

Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables. It is shown that the corresponding dynamical system describes, within Ostrogradski framework, the nonrelativistic particle obeying (N+1)-th order equation of motion. As a special case, the Schroedinger group and the standard Newton equations are obtained for N=1 (l=1/2).Comment: 18 pages, no figures; few references adde

Free Particle Wave Function and Niederer's Transformation

The solutions to the free Schroedinger equation discussed by P. Strange (arXiv: 1309.6753) and A. Aiello (arXiv: 1309.7899) are analyzed. It is shown that their properties can be explained with the help of Niederer's transformation

A note on the Hamiltonian formalism for higher-derivative theories

An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian is nonsingular and the Legendre transformation is performed in a straightforward way.Comment: 8 pages, no figure

N-Galilean conformal algebras and quantum theory with higher order time derivatives

It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the Schrodinger equation corresponding to the free Lagrangian involving (N+1)/2-th order time derivatives.Comment: references update

Nonrelativistic conformal transformations in Lagrangian formalism

The conformal transformations corresponding to $N$-Galilean conformal symmetries, previously defined as canonical symmetry transformations on phase space, are constructed as point transformations in coordinate space

On dynamical realizations of l-conformal Galilei groups

We consider the dynamics invariant under the action of l-conformal Galilei group using the method of nonlinear realizations. We find that by an appropriate choice of the coset space parametrization one can achieve the complete decoupling of the equations of motion. The Lagrangian and Hamiltonian are constructed. The results are compared with those obtained by Galajinsky and Masterov [Nucl. Phys. B860, (2013), 212].Comment: 16 pages, no figures; substantial improvements of the text; several typos corrected; accepted for publication in Nucl. Phys.

Canonical formalism and quantization of perturbative sector of higher-derivative theories

The theories defined by Lagrangians containing second time derivative are considered. It is shown that if the second derivatives enter only the terms multiplied by coupling constant one can consistently define the perturbative sector via Dirac procedure. The possibility of introducing standard canonical variables is analysed in detail. The ambiguities in quantization procedure are pointed out