Related papers: Duality symmetries behind solutions of the classic…
We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling…
In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these…
Here we show that the concepts behind such terms as entanglement, qubits, quantum gates, quantum error corrections, unitary time evolution etc., which are usually ascribed to quantum systems, can be adequately realized on a set of coupled…
The classical two-dimensional one-component plasma is an exactly solvable model, at some special temperature, even when the one-body potential acting on the particles has a quadrupolar term. As a supplement to a recent work of Di Francesco,…
The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non--abelian theories. Possible applications of these solutions to…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
We consider the relationship between symmetries of two-dimensional autonomous dynamical system in two common formulations; as a set of differential equations for the derivative of each state with respect to time, and a single differential…
We propose a general exact method of calculating dynamical correlation functions in dual symplectic brick-wall circuits in one dimension. These are deterministic classical many-body dynamical systems which can be interpreted in terms of…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
The Dirac equation in spherically symmetric fields is separated in two different tetrad frames. One is the standard cartesian (fixed) frame and the second one is the diagonal (rotating) frame. After separating variables in the Dirac…
The existence of elliptic periodic solutions of a perturbed Kepler problem is proved. The equations are in the plane and the perturbation depends periodically on time. The proof is based on a local description of the symplectic group in two…
The usual methods for formulating and solving the quantum mechanics of a particle moving in a magnetic field respect neither locality nor any global symmetries which happen to be present. For example, Landau's solution for a particle moving…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
We show that the Einstein equations in the vacuum are invariant under an $SO(2)$ duality symmetry which rotates the curvature 2-form into its tangent space Hodge dual. Akin to electric-magnetic duality in gauge theory, the duality operation…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is…
The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are…
We construct, in classical two-time physics, the necessary structure for the most general configuration space formulation of quantum mechanics containing gravity in d+2 dimensions. This structure is composed of a symmetric Riemannian metric…
The geometrical structure and the quantum properties of the recently proposed harmonic space action describing self-dual Yang-Mills (SDYM) theory are analyzed. The geometrical structure that is revealed is closely related to the twistor…