Exact vector potential integrals are written in spherical coordinates for the CWTHA. From these the far fields are expressed, both for the CWTHA (dipole field) and for a single winding (loop field). The vector potentials are numerically integrated; the results give the dipole field for a given current and ratio of dipole field to loop field.

Of concern are the minimal and maximal operators on L2(R") associated with the differential expression Te = J2{id/dxJ + qJ{x))2 + W{x) j=i where (q.#„) = gradQ for some real function W on R" and W satisfies ¿M-2 < W(Jf) < C|x|~2 . In particular, for Q = 0, Xq reduces to the singular Schrödinger operator -A+ W{x). Among other results, it is shown that the maximal operator (associated with the xq...

For the feature analysis of vector fields we decompose a given vector field into three components: a divergence-free, a rotation-free, and a harmonic vector field. This Hodgetype decomposition splits a vector field using a variational approach, and allows to locate sources, sinks, and vortices as extremal points of the potentials of the components. Our method applies to discrete tangential vect...

A bstract We embed Nelson’s theory of stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative quantum mechanics on (pseudo-)Riemannian manifolds. Within this approach, we derive differential equations for massive spin-0 test particles charged under scalar potentials, vector potentials and gravity. Furthermore, associated Schrödinger equati...

Alexander L. Kitt,1,* Vitor M. Pereira,2,† Anna K. Swan,1,3,4,‡ and Bennett B. Goldberg1,4,5,§ 1Department of Physics, Boston University, 590 Commonwealth Ave, Boston, Massachusetts 02215, USA 2Graphene Research Center and Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 3Department of Electrical and Computer Engineering, Boston University, 8 St Mary’...

We demonstrate reverse-time imaging using multicomponent elastic wavefields. The elastic data are used as boundary conditions for a numeric solution to the elastic wave-equation solved using a staggeredgrid finite-difference implementation. P and S components are not separated from recorded data, but are extrapolated together as part of a vector wavefield. A straightforward extension to the cro...

In this paper, we focus on the representation of a divergence-free vector field, defined, on a connected nonsimply connected domain Ω ⊂ R3 with a connected boundary Γ, by its curl and its normal component on the boundary. The considered problem is discretized with H(curl)and H(div)-conforming finite elements. In order to ensure the uniqueness of the vector potential, we propose a spanning tree ...

Abstract. In this paper, we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the L transition probability amplitude via improper Riemann integrals. Our formulation will hold for vector potential Hamiltonian for which its potential and vector potential each c...

The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz’s theorem. It is found, however, that the theorem fails in most practical instances. Other methods to find the potentials – as pursued in plasma physics – are e...

We prove asymptotic completeness for operators of the form H = −∆+L on L(R), d ≥ 2, where L is an admissible perturbation. Our class of admissible perturbations contains multiplication operators defined by real-valued potentials V ∈ L(R), q ∈ [d/2, (d + 1)/2] (if d = 2 then we require q ∈ (1, 3/2]), as well as real-valued potentials V satisfying a global Kato condition. The class of admissible ...