Joanna Gonera

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.

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. B866, (2013), 212].

Euclidean Path Integral and 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

Modified Hamiltonian formalism for higher-derivative theories

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.

On the triviality of higher-derivative theories

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.

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 Niederers transformation.

Canonical formalism and quantization of the 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.

Nonlinear realizations and the orbit method

Given a symmetry group one can construct the invariant dynamics using the technique of nonlinear realizations or the orbit method. The relationship between these methods is discussed. Few examples are presented.

N-Conformal Galilean Group as a Maximal Symmetry Group of Higher-Derivative Free Theory

It is shown that for N odd the N-conformal Galilean algebra is the algebra of maximal Noether symmetry group, both on the classical and quantum level, of free higher derivative dynamics.

Comment on “Functional determinants in higher derivative Lagrangian theories” [J. Math. Phys. 50, 103517 (2009)]

We comment on the recent paper of Di Criscienzo and Zerbini [J. Math. Phys. 50, 103517 (2009)]. We argue that the Euclidean evolution operator computed in our paper (K. Andrzejewski et al., e-print arXiv:0904.3055) is correct contrary to the claim of Di Criscienzo and Zerbini.