arXiv subjects

Zahra Molaee

Publications and source records attributed to Zahra Molaee.

10 recordsLinked to original sources

arXiv2026

Stability and Chaotic Dynamics in a Nonlinearly Confined ghost-sector Hamiltonian

We investigate the nonlinear dynamics of a Hamiltonian system containing a ghost degree of freedom coupled to a canonical sector through nonlinear interactions. The model consists of one positive-energy and one negative-energy mode, augmented by quartic and sextic nonlinearities that regularize the large-amplitude behavior of the system. Unlike conventional ghost models, which typically exhibit runaway trajectories due to the indefinite nature of the kinetic energy, the present Hamiltonian possesses a confining nonlinear structure that renders the accessible energy surfaces compact for finite total energy. We derive the equations of motion and analyze the geometric properties of the Hamiltonian flow. Particular attention is devoted to the interplay between local ghost-induced instability and global nonlinear confinement. We show that the sextic contribution dominates the asymptotic dynamics and prevents escape to infinity despite the presence of a negative-energy sector. As a consequence, the model provides a controlled framework for studying bounded dynamics in ghost-coupled systems. The phase-space structure is investigated through numerical integration, Poincaré surfaces of section, and Lyapunov analysis. Depending on the interaction strength and nonlinear couplings, the system exhibits a transition from regular quasi-periodic motion to chaotic dynamics characterized by positive maximal Lyapunov exponents. Remarkably, chaotic trajectories remain confined within compact regions of phase space, yielding a realization of bounded chaotic motion in a ghost-containing Hamiltonian system. These results provide a concrete example of how nonlinear self-interactions can regularize ghost dynamics at the classical level and indicate a useful prototype for studying stability, confinement, and chaos in nonstandard Hamiltonian theories.

hep-th↗

arXiv2026

Bounded Chaos in a Ghost-Coupled Hamiltonian System

We study the dynamics of a Hamiltonian system with a ghost degree of freedom, characterized by a negative kinetic-energy contribution and the possibility of runaway behavior due to an indefinite energy functional. We present numerical evidence that a nonlinear interaction term, together with a saturating exponential potential $V_c$, can suppress phase-space escape over the parameter ranges explored in this work. Using direct numerical integration of the Hamiltonian equations of motion, Poincaré surfaces of section, and trajectory projections, we find that the ghost sector and nonlinear couplings generate a mixed phase-space structure with both regular islands and chaotic regions. The maximal Lyapunov exponent supports bounded chaotic motion: nearby trajectories separate exponentially while remaining confined to a finite region of phase space for the investigated initial conditions and parameters $(\varepsilon,α)$. These results suggest that nonlinear confinement can significantly alter the stability properties of negative-energy sectors at the classical level. They provide numerical evidence for a bounded-chaos regime in which ghost-induced divergences are avoided within the explored domain.

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arXiv2025

Generators of Local Lorentz Transformation in ADM-Vielbein Formalism of Gravitational Relativity

General relativity contains 16 variables in the framework of ADM-Vielbein formalism which are 6 more than metric formalism. These variables emerge due to additional symmetry of Local Lorentz Transformations. In the framework of the Hamiltonian approach, it is expected to find first class constraints which generate this gauge symmetry. We introduce the complete form of such constraints and show that they exactly obey the algebra of the Lorentz group.

gr-qc↗

arXiv2023

Constraint structure of the Generalized Proca model in the Lagrangian formalism

We present a new Lagrangian approach for the dynamical structure of the generalized Proca theory (GP). This approach includes the A-Z constraint structure of the model in the Lagrangian formalism and ends up with an accurate count of the number of degrees of freedom. We also give the complete Hamiltonian constraint structure of the model.

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arXiv2022

Multi-field Cuscuton Cosmology

In this paper, we first introduce a multi-field setup of Cuscuton gravity in a curved field space manifold. Then, we show that this model allows for a regular bouncing cosmology and it does not lead to ghosts or other instabilities at the level of perturbations. More precisely, by decomposing the scalar fields perturbations into the tangential and normal components with respect to the background field space trajectory, the entropy mode perpendicular to the background trajectory is healthy which directly depends on the signature of the field-space metric, whereas the adiabatic perturbation tangential to the background trajectory is frozen. In analogy with the standard Cuscuton theory equipped with an extra dynamical scalar field, the adiabatic field does not have its own dynamics, but it modifies the dynamics of other dynamical fields like entropy mode in our scenario. Finally, we perform a Hamiltonian analysis of our model in order to count the degrees of freedom propagated by dynamical fields.

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arXiv2022

Multi-field Mimetic Gravity

In this paper, we extend the mimetic gravity to the multi-field setup with a curved field space manifold. The multi-field mimetic scenario is realized via the singular limit of the conformal transformation between the auxiliary and the physical metrics. We look for the cosmological implications of the setup where it is shown that at the background level the mimetic energy density mimics the roles of dark matter. At the perturbation level, the scalar field perturbations are decomposed into the tangential and normal components with respect to the background field space trajectory. The adiabatic perturbation tangential to the background trajectory is frozen while the entropy mode perpendicular to the background trajectory propagates with the speed of unity. Whether or not the entropy perturbation is healthy directly depends on the signature of the field-space metric. We perform the full non-linear Hamiltonian analysis of the system with the curved field space manifold and calculate the physical degrees of freedom verifying that the system is free from the Ostrogradsky-type ghost.

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arXiv2021

Hamiltonian formalism of the ghost free Tri(-Multi)gravity theory

We study the Hamiltonian structure of tri-gravity and four-gravity in the framework of ADM decomposition of the corresponding metrics. Hence we can deduce the general structure of the constraint system of multi-gravity. We will show it is possible and consistent to assume additional constraints which provide the needed first class constraints for generating diffeomorphism as well as enough second class constraints to omit the ghosts.

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arXiv2021

Gauge generator for bi-gravity and multi-gravity models

Following the Hamiltonian structure of bi-gravity and multi-gravity models in the full phase space, we have constructed the generating functional of diffeomorphism gauge symmetry. As is expected, this generator is constructed from the first class constraints of the system. We show that this gauge generator works well in giving the gauge transformations of the canonical variables.

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arXiv2019

Hamiltonian structure of bi-gravity, problem of ghost and bifurcation

We analyze the Hamiltonian structure of a general theory of bi-gravity where the interaction term is a scalar function of the form $ V(\mathcal{X}^{n}) $ where $ \mathcal{X} $ may be $\sqrt{g^{-1}f} $ or $ g^{-1}f $. We give necessary conditions for the interaction term of such a theory to be ghost free. We give a precise constraint analysis of the bi-gravity theory of Hassan- Rosen and show that the additional constraint which omit the ghost is just one possibility at the bifurcation point.

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arXiv2018

Massive gravity, canonical structure and gauge symmetry

Performing Hamiltonian analysis of the massive gravity [9] in full phase space, we see that the theory is ghost free. We also see in a more clear way that this result is intrinsic of the interaction term and does not depend on the variables involved. Since no first class constraint emerges, the theory seems to lack gauge symmetry. We show that this is due to the presence of an auxiliary field, and the symmetry may be manifest in the Stuckelberg formulation. We give the generating functional of gauge transformation in this model.

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