Related papers: The Square Cat
We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
We deform two-dimensional topological gravity by making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once…
The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent…
In the history of mechanics, there have been two points of view for studying mechanical systems: The Newtonian and the Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order…
Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved…
Geometrical properties of three-body orbits with zero angular momentum are investigated. If the moment of inertia is also constant along the orbit, the triangle whose vertexes are the positions of the bodies, and the triangle whose…
Biological organisms swimming at low Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper we present an analysis of locomotion near a free surface with surface tension. Using a…
Consider the spatial Newtonian three body problem at fixed negative energy and fixed angular momentum. The moment of inertia $I$ provides a measure of the overall size of a three-body system. We will prove that there is a positive number…
The Rattleback is a very popular science toy shown to students all over the world to demonstrate the non-triviality of rotational motion. When spun on a horizontal table, this boat-shaped object behaves in a peculiar way. Although the…
First, the properties of a classical model of spontaneous symmetry breakdown are analyzed. Then, the pros and cons of some pedagogical non-relativistic quantum-mechanical models, also used to illustrate spontaneous symmetry breakdown, are…
We show that the Power-Zienau-Woolley picture of the electrodynamics of nonrelativistic neutral particles (atoms) can be derived from a gauge-invariant Lagrangian without making reference to any gauge whatsoever in the process. This…
Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space…
In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference…
A universal inequality that bounds the angular momentum of a body by the square of its size is presented and heuristic physical arguments are given to support it. We prove a version of this inequality, as consequence of Einstein equations,…
We suggest to use "minimal" choice of quantum gravity theory, that is the quantum field theory, in which space-time is seen as Riemannian space and metric (or vierbein field) is the dynamical variable. We then suggest to use the simplest…
An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude…
We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…
Using as inspiration the well known chiral effective lagrangian describing the interactions of pions at low energies, in these lectures we review the quantization procedure of Einstein gravity in the spirit of effective field theories. As…
In [Arch. Ration. Mech. Anal. 213 (2014), 981-991] it has been proved that in the Newtonian $N$-body problem, given a minimal central configuration $a$ and an arbitrary configuration $x$, there exists a completely parabolic orbit starting…