Related papers: Mirror potentials in classical mechanics
In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.
The modified scalar boson propagator due to the presence of a hyperplane semi-transparent mirror is computed. From this, the classical interaction between static charges and the mirror is investigated employing delta-like potentials and…
The curvature of the inertial or gravitational potentials defined as a Hodge-Helmholtz decomposition of acceleration into an irrotational and a solenoidal components, enable to federate certain domains of macroscopic physics. After two…
The mean force exerted upon a perfect mirror moving in vacuum in a two dimensional spacetime has the same expression as the radiation reaction force computed in classical electron theory. It follows that unacceptable runaway solutions are…
A projective mirror polyhedron is a projective polyhedron endowed with reflections across its faces. We construct an explicit diffeomorphism between the moduli space of a mirror projective polyhedron with fixed dihedral angles in…
We consider the quantum radiation from a partially reflecting moving mirror for the massless scalar field in 1+1 Minkowski space. Partial reflectivity is achieved by localizing a delta-type potential at the mirror's position. The radiated…
Moduli with flat or run-away classical potentials are generic in theories based on supersymmetry and extra dimensions. They mix between themselves and with matter fields in kinetic terms and in the nonperturbative superpotentials. As the…
The anti self-adjoint operators of coordinate and momentum are introduced and applied in discussion of tunneling through the potential barrier where imaginary value of momentum unavoidably appears. Tunneling through temporal barrier is…
We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable…
Small objects floating on a fluid have a tendency to aggregate due to capillary forces. This effect has been used, with the help of a magnetic induction field, to assemble submillimeter metallic spheres into a variety of structures, whose…
We give an integral expression for the vector potential of a time-independent, steady azimuthal current density. Our derivation is substantially simpler and somewhat more general than others given in the literature. As an illustration, we…
The path integral formulation of quantum mechanics constructs the propagator by evaluating the action S for all classical paths in coordinate space. A corresponding momentum path integral may also be defined through Fourier transforms in…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
We calculate the flux from a spherical mirror which is expanding or contracting with nearly uniform acceleration. We find that the flux at an exterior point (which could in principle be a functional of the mirror's past history) is actually…
We consider the algebra associated to a group of transformations which are symmetries of a regular mechanical system (i.e. system free of constraints). For time dependent coordinate transformations we show that a central extension may…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
Trajectories in logarithmic potentials are investigated by taking as example the motion of an electron within a cylindrical capacitor. The solution of the equation of motion in plane polar coordinates, (r,{\phi}) is attained by forming a…
Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the…
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and…
The tools developed in a preceding article for interpreting spacetime geometry in terms of all possible space-plus-time splitting approaches are applied to circular orbits in some familiar stationary axisymmetric spacetimes. This helps give…