K. Andrzejewski

Conformal Newton–Hooke symmetry of Pais–Uhlenbeck oscillator

K.A. and J.G. are grateful to Piotr Kosinski for helpful and illuminating discussions. We thank Peter Horvathy and Andrei Smilga for useful correspondence. This work was sup-ported by the NCN grant DEC-2013/09/B/ST2/02205 (K.A. and J.G.) and by the RFBR grants 13-02-90602-Arm (A.G.) and 14-02-31139-Mol (I.M.) as well as by the MSU program “Nauka” under the project 825 (A.G. and I.M.). I.M. gratefully acknowledges the support of the Dynasty Foundation. ©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3.

Conformal Newton–Hooke algebras, Niederer's transformation and Pais–Uhlenbeck oscillator

Special thanks are to Piotr Kosinski for valuable comments and suggestions. The discussions with Joanna Gonera and Pawel Maślanka are gratefully acknowledged. The work is supported by the grant of National Research Center number DEC-2013/09/B/ST2/ 02205.

Nonrelativistic conformal transformations in Lagrangian formalism

The conformal transformations corresponding to

On dynamical realizations of l-conformal Galilei groups

N

Newton-Hooke type symmetry of anisotropic oscillators ∗

-Galilean conformal symmetries, previously defined as canonical symmetry transformations on phase space, are constructed as point transformations in coordinate space.

Euclidean Path Integral and Higher-Derivative Theories

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. B866, (2013), 212].

Modified Hamiltonian formalism for higher-derivative theories

Abstract Rotation-less Newton–Hooke-type symmetry, found recently in the Hill problem, and instrumental for explaining the center-of-mass decomposition, is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton–Hooke symmetry is recovered in the isotropic case. Star escape from a galaxy is studied as an application.

On the triviality of higher-derivative theories

We consider the Euclidean path integral approach to higher-derivative theories proposed by Hawking and Hertog (Phys. Rev. D 65 (2002), 103515). The Pais-Uhlenbeck oscillator is studied in some detail. The operator algebra is reconstructed and the structure of the space of states is revealed. It is shown that the quantum theory results from quantizing the classical complex dynamics in which the original dynamics is consistently immersed. The field-theoretical counterpart of Pais-Uhlenbeck oscillator is also considered. Subject Index: 013, 064

Generalized Niederer's transformation for quantum Pais–Uhlenbeck oscillator

An alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach, it has the following advantages: (i) The Lagrangian, when expressed in terms of new variables, yields proper equations of motion; no additional Lagrange multipliers are necessary. (ii) The Legendre transformation can be performed in a straightforward way, provided the Lagrangian is nonsingular in the Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.

Free-particle wave function and Niederer's transformation

Abstract The higher-derivative theories with degenerate frequencies exhibit BRST symmetry [V.O. Rivelles, Phys. Lett. B 577 (2003) 147]. In the present Letter meaning of BRST-invariance condition is analyzed. The BRST symmetry is related to nondiagonalizability of the Hamiltonian and it is shown that BRST condition singles out the subspace spanned by proper eigenvectors of the Hamiltonian.