Related papers: On exactly solvable higher-derivative systems
Ghost fields in quantum field theory have been a long-standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
The unphysical spin-2 massive degrees of freedom in higher derivative gravity may be either massive unphysical ghosts or tachyonic ghosts. In the last case there is no Planck-scale threshold protecting vacuum cosmological solutions from…
A wide class of Hamiltonian systems with N degrees of freedom and endowed with, at least, (N-2) functionally independent integrals of motion in involution is constructed by making use of the two-photon Lie-Poisson coalgebra. The set of…
We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective…
The classical trajectories of a particle governed by the PT-symmetric Hamiltonian $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) have been studied in depth. It is known that almost all trajectories that begin at a classical turning point…
Ostrogradsky theorem states that Hamiltonian is unbounded when Euler-Lagrange equations are higher than second-order differential equations under the nondegeneracy assumption. Since higher-order nondegenerate Lagrangian can be always recast…
The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
We study the classical solutions of three dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first order formulation. The action of higher spin TMG has been proposed in arXiv:1110.5113 to be of a…
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit…
We present an example of an integrable Hamiltonian system with scalar potential in the three-dimensional Euclidean space whose integrals of motion are quadratic polynomials in the momenta, yet its Hamilton-Jacobi / Schrodinger equation…
The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…
We compare a relativistic and a nonrelativistic version of Ostrogradsky's method for higher-time derivative theories extended to scalar field theories and consider as an alternative a multi-field variant. We apply the schemes to space-time…
We analyze the perturbative implications of the most general high derivative approach to quantum gravity based on a diffeomorphism invariant local action. In particular, we consider the super-renormalizable case with a large number of…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian…
We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $\sigma$-model with cosmological constant. The $\sigma$-model can be perceived as exterior configuration of a spontaneously-broken $SO(D-1)$ global…
A broad class of higher dimensional instanton solutions are found for a theory which contains gravity, a scalar field and antisymmetric tensor fields of arbitrary rank. The metric used, a warp product of an arbitrary number of any compact…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…