相关论文: Functional Determinants in Higher Derivative Lagra…

We investigate the cosmological dynamics of scalar fields governed by higher-order gravity, with particular emphasis on models inspired by the Pais-Uhlenbeck oscillator--a prototypical fourth-order system known for its connection to…

Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical…

Given any (Feynman) propagator which is Lorentz and translation invariant, it is possible to construct an action functional for a scalar field such that the quantum field theory, obtained by path integral quantization, leads to this…

Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the…

We prove that higher-derivative and genuinely nonlocal Lagrangian systems can be Lyapunov-stable even when their Hamiltonians lack a lower bound. Explicit free and coupled Pais-Uhlenbeck oscillators, together with a genuine nonlocal model,…

Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most…

We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of…

We discuss the quantum dynamics of the Pais-Uhlenbeck oscillator. The Lagrangian of this higher-derivative model depends on two frequencies. When the frequencies are different, the free PU oscillator has a pure point spectrum that is dense…

Shortcomings of Dirac's constrained analysis in the context of fourth order Pais-Uhlenbeck oscillator action and the appearance of badly affected phase-space Hamiltonian for a generalized fourth order oscillator action, following…

We consider the class of higher derivative field equations whose wave operator is a square of another self-adjoint operator of lower order. At the free level, the models of this class are shown to admit a two-parameter series of integrals…

We consider a Hamiltonian formulation of the (2n+1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether…

We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian, as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be…

We introduce a new class of higgs type complex-valued scalar fields $U$ with Feynman propagator $\sim 1/p^4$ and consider the matching to the traditional fields with propagator $\sim 1/p^2$ in the viewpoint of effective potentials at tree…

We extend the perturbative approach developed in an earlier work to deal with Lagrangians which have arbitrary higher order time derivative terms for both bosons and fermions. This approach enables us to find an effective Lagrangian with…

We provide a complete classification of all the ways the Pais-Uhlenbeck osicllator might be embedded in two dimensional space. We discuss the Bi-Hamiltonian structures of this model, and examine how alternative Hamiltonian structures might…

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian…

A system of two independent Bosonic Harmonic Oscillators is converted into the respective fourth-order derivative Pais-Uhlenbeck oscillator model. The conversion procedure displays transparently how the quantization of the fourth-order…

Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator using complex canonical transformations. We show that starting from a Lagrangian approach we obtain a transformation that makes the extended PU oscillator, with…

The problems that are connected with Lagrangians which depend on higher order derivatives (namely additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of…

We study stability of higher-derivative dynamics from the viewpoint of more general correspondence between symmetries and conservation laws established by the Lagrange anchor. We show that classical and quantum stability may be provided if…