Related papers: Quantizing with a higher time derivative
The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl. Phys. B 885 (2014) 150] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck…
The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this…
Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. In this…
We refine the presentation of the previous paper of our group, Y.Ezawa et al., Class. Quantum Grav. {\bf 23} (2006), 3205 [arXiv:gr-qc/0507060]. In that paper, we proposed a canonical formalism of f(R)-type generalized gravity by using the…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges and…
Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the $4-\epsilon$ renormalization group for this theory, an approach…
We introduce new models of f(R) theories of gravity that are generalization of Horava-Lifshitz gravity.
We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic…
Certain difficulties of quantum gravity can be avoided if we embed the spacetime $V_4$ into a higher dimensional space $V_N$; then our spacetime is merely a 4-surface in $V_N$.What remains is conceptually not so difficult: just to quantise…
The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model…
It is often argued that gravity has to be a quantum theory simply because a fundamentally semiclassical approach would necessarily be inconsistent. Here I review recent Newtonian toy models of (stochastic) semiclassical gravity. They…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
A canonical formalism of f(R)-type gravity is proposed, resolving the problem in the formalism of Buchbinder and Lyakhovich(BL). The new coordinates corresponding to the time derivatives of the metric are taken to be its Lie derivatives…
We study the quantum Pais-Uhlenbeck oscillator at the resonant (equal-frequency) point, where the dynamics becomes non-diagonalisable and the conventional Fock-space construction collapses. At the classical level, the degenerate system…
We construct the classical dynamical system which has a quantum-like behavior. We have shown that the energy-time uncertainty relation takes place for the system and it has purely classical nature. We investigate the behavior of the system…
We describe postulates for a novel realist version of relativistic quantum theory or quantum field theory in Minkowski space or other background spacetimes with suitable asymptotic properties. We illustrate their application in toy models.
The classical and quantum oscillator model on Lie-algebraically deformed nonrelativistic space-time is introduced and analyzed. The corresponding equations of motions are studied using mostly numerical methods. The time-dependent energy…