Related papers: Hamilton-Jacobi formalism for Generalized Chaplygi…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
We generalize the existing works on the way (generalized) LTB models can be embedded into polymerized spherically symmetric models in several aspects. We re-examine such an embedding at the classical level and show that a suitable LTB…
The O(3) non-linear sigma model is investigated using multi Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac's method. By choosing an adequate extension…
In this present work, we try to build up a cosmological model using a non-canonical scalar field within the framework of a spatially flat FRW space-time. In this context, we have considered four different parametrizations of the equation of…
A detailed Hamilton-Jacobi analysis for linearized $\lambda R$ gravity is developed. The model is constructed by rewriting linearized gravity in terms of a parameter $\lambda$ and new variables. The set of all hamiltonians is identified…
The non-abelian generalization of the Born-Infeld non-linear lagrangian is extended to the non-commutative geometry of matrices on a manifold. In this case not only the usual SU(n) gauge fields appear, but also a natural generalization of…
We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be…
Using $\delta N$ formalism, in the context of a generic multi-field inflation driven on a non-flat field space background, we revisit the analytic expressions of the various cosmological observables such as scalar/tensor power spectra,…
We study the Hamilton formalism for Connes-Lott models, i.e., for Yang-Mills theory in non-commutative geometry. The starting point is an associative $*$-algebra $\cA$ which is of the form $\cA=C(I,\cAs)$ where $\cAs$ is itself a…
In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lema\^{\i}tre-Robertson-Walker, de…
Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
The dynamic status of scalar fields is studied in the Hamiltonian approach to the General Relativity. We show that the conformal coupling of the scalar field violates the standard geometrical structure of the Einstein equations in GR and…
In this paper we propose a Hamilton-Jacobi theory for implicit contact Hamiltonian systems in two different ways. One is the understanding of implicit contact Hamiltonian dynamics as a Legendrian submanifold of the tangent contact space,…
We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.
The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential $\rm V(\phi)$ in the scalar field inflation scenario. The Bohmian approach (a WKB-like formalism) was employed in order to constraint a generic form of…
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
The present work investigates several models of a single real scalar field, engendering kinetic term of the Dirac-Born-Infeld type. Such theories introduce nonlinearities to the kinetic part of the Lagrangian, which presents a square root…
A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…