Related papers: Homotopy Invariants and Time Evolution in (2+1)-Di…
In this paper we introduce a definition of time that emerges in terms of the geometry of the configuration space of a dynamical system. We illustrate this, using the Hamilton-Jacobi equation, in various examples: particle mechanics on a…
We discuss some families of integrable and superintegrable systems in $n$-dimensional Euclidean space which are invariant to $m\geq n-2$ rotations. The integrable invariant Hamiltonian $H=\sum p_i^2+V(q)$ commutes with $n-2$ integrals of…
We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is…
We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the…
We study a general class of models whose classical Hamiltonians are given by H = U(x) p + V(x)/p, where x and p are the position and momentum of a particle moving in one dimension, and U and V are positive functions. This class includes the…
A gauge and diffeomorphism invariant theory in (2+1)-dimensions is presented in both first and second order Lagrangian form as well as in a Hamiltonian form. For gauge group $SO(1,2)$, the theory is shown to describe ordinary Einstein…
Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system…
The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant…
The initial data in the polygon approach to (2+1)D gravity coupled to point particles are constrained by the vertex equations and the particle equations. We establish the hyperbolic nature of the vertex equations and derive some…
In a slight different way from the previous one, we propose a modified non-Euclidian transformation on the SO(2N+2)/U(N+1) Grassmannian which give the projected SO(2N+1) Tamm-Dancoff equation. We derive a classical time dependent (TD)…
In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate…
Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini…
We use a systematic construction method for invariant connections on homogeneous spaces to find the Einstein-SU(n)-Yang-Mills equations for Friedmann-Robertson-Walker and locally rotationally symmetric homogeneous cosmologies. These…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
A covariant Hamiltonian description of Palatini's gravity on manifolds with boundary is presented. Palatini's gravity appears as a gauge theory satisfying a constraint in a certain topological limit. This approach allows the consideration…
A class of integrable models of 1+1 dimensional dilaton gravity coupled to scalar and electromagnetic fields is obtained and explicitly solved. More general models are reduced to 0+1 dimensional Hamiltonian systems, for which two integrable…
In this work we present the general unified description for the unitary time-evolution generated by time-dependent non-Hermitian Hamiltonians embedding the bosonic representations of $\mathfrak{su}(1,1)$ and $\mathfrak{su}(2)$ Lie algebras.…
We consider the formulation of entropic gravity in two spacetime dimensions. The usual gravitational force law is derived even in the absence of area, as normally required by the holographic principle. A special feature of this perspective…
This paper is a review of the relationship between the metric formulation of (2+1)-dimensional gravity and the loop observables of Rovelli and Smolin. I emphasize the possibility of reconstructing the geometry, via the theory of geometric…