Search results for "Vector Potential"
showing 10 items of 31 documents
Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets
2017
We present the generalized quasiclassical theory of the long-range superconducting proximity effect in heterostructures with strong ferromagnets, where the exchange splitting is of the order of Fermi energy. In the ferromagnet the propagation of equal-spin Cooper pairs residing on the spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian gauge field which results either from the spin-orbital coupling or from the magnetic texture. This additional gauge field enters into the quasiclassical equations in superposition with the usual electromagnetic vector potential and results in the generation of spontaneous superconducting currents and phase shifts in various geometr…
On electric and magnetic problems for vector fields in anisotropic nonhomogeneous media
1983
r= 3~2, initiated by Saranen [ 131. In the above, n is the outward-drawn unit normal to the boundary and A denotes the exterior product. According to the simple models for static magnetic fields (resp. electric fields) which are governed by (0.1) (resp. (0.2)), we call (0.1) the magnetic type problem and (0.2) the electric type problem. Considering bounded smooth domains a c R3, we discussed in [ 131, by means of an appropriate Hilbert space method, the solvability and the representation of the solutions for both problems (0.1) and (0.2). Such a new approach was necessary to cover the general nonhomogeneous cases where v and E are matrix-valued functions. Here our aim is twofold. First, we …
Chiral anomalies in even and odd dimensions
1985
Odd dimensional Yang-Mills theories with an extra ‘topological mass” term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.
Effective-Lagrangian formulation of generalized vector dominance. II
1975
As in a preceding paper we generalize the Lagrangian of Lee and Zumino to include several mutually interacting vector mesons. The treatment is more general in the sense that all possible interactions between the vector mesons, compatible with the field-current proportionality relations, are now discussed. It is moreover demonstrated that also the fields corresponding to the physical vector mesons satisfy a field-current proportionality relation of exactly the same form. Comparison of the different schemes and their implications for the magnetic moments of the vector mesons are discussed.
Minimal unit vector fields
2002
We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.
Volume, energy and generalized energy of unit vector fields on Berger spheres: stability of Hopf vector fields
2005
We study to what extent the known results concerning the behaviour of Hopf vector fields, with respect to volume, energy and generalized energy functionals, on the round sphere are still valid for the metrics obtained by performing the canonical variation of the Hopf fibration.
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
1987
AbstractA cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate toWe define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent toOur main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to
General duality in vector optimization
1993
Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x 0 ∊ A w,0 ∊ Fx$0 such that w,0 is minimal in FA. To a family of vector minimization problemsminimize , one associates a Lagrange relation where ξ belongs to an arbitrary class Ξ of mappings, the main purpose being to recover solutions of the original problem from the vector minimization of the Lagrange relation for an appropriate ξ. This ξ turns out to be a solution of a dual vector maximization problem. Characterizations of exact and approximate duality in terms of vector (generalized with respect to Ξ) convexity and subdifferentiability are given. They extend the theory existin…
Biorthonormal-basis method for the vector description of optical-fiber modes
1998
This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.
The electromagnetic and Proca fields revisited: A unified quantization
1997
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μφ(x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U(1)(x, t), acquire dyn…