Journal ArticleDOI
Comments on the structural features of the Pais-Uhlenbeck oscillator
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In this article, the Jacobi last multiplier (JLM) was used to derive the Lagrangian of a fourth-order differential equation and the Hamiltonian of the Pais-Uhlenbeck problem.Abstract:
We explore the Jacobi last multiplier (JLM) as a means for deriving the Lagrangian of a fourth-order differential equation. In particular, we consider the classical Pais– Uhlenbeck problem and write down the accompanying Hamiltonian. We then compare such an expression with our alternative derivation of the Hamiltonian that makes use of the Ostrogradski’s method and show how a mapping from the one to the other is achievable by variable transformations.read more
Citations
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Book ChapterDOI
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS
Journal ArticleDOI
Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
TL;DR: In this article, the author is grateful to Joanna Gonera, Piotr Kosinski and Pawel Maślanka for useful comments discussions with Professors Anton Galajinsky and Ivan Masterov.
Journal ArticleDOI
The odd-order Pais-Uhlenbeck oscillator
TL;DR: In this paper, a Hamiltonian formulation of the (2n + 1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation is considered.
Journal ArticleDOI
Generalized Niederer's transformation for quantum Pais-Uhlenbeck oscillator
TL;DR: In this paper, the quantum counterpart of the transformation which maps the free higher derivatives theory into the Pais-Uhlenbeck oscillator is constructed, and some consequences of this transformation are discussed.
Journal ArticleDOI
Markov constant and quantum instabilities
TL;DR: For a qualitative analysis of the spectra of two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful as mentioned in this paper, and the results may inspire methodical innovations ranging from the description of the stability properties of metamaterials and of hiddenly unitary quantum evolution models up to the clarification of the mechanisms of occurrence of ghosts in quantum cosmology.
References
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Book
A treatise on the analytical dynamics of particles and rigid bodies
TL;DR: In this article, a comprehensive account of analytical dynamics is given, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration and dissipative systems.
Book ChapterDOI
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS
Journal ArticleDOI
On Field Theories with Non-Localized Action
A. Pais,G. E. Uhlenbeck +1 more
TL;DR: In this paper, it was investigated whether suitable generalizations of the field equations of current field theories to equations of higher order may be of help in eliminating the divergent features of the present theory.
Journal ArticleDOI
No-Ghost Theorem for the Fourth-Order Derivative Pais-Uhlenbeck Oscillator Model
TL;DR: A new realization of the fourth-order derivative Pais-Uhlenbeck oscillator is constructed that possesses no states of negative norm and has a real energy spectrum that is bounded below.
Journal ArticleDOI
The Problem of Nonlocality in String Theory
D. A. Eliezer,R. P. Woodard +1 more
TL;DR: In this paper, the authors discuss the problems associated with the essential nonlocality of all string field actions in light cone theories and show that these problems are invisible to perturbative analysis.