Wave Equation For Spin Research Articles

Complete sets of functions for perturbations of Robertson Walker cosmologies

Crucial to a knowledge of the perturbations of Robertson Walker cosmological models is a knowledge of complete sets of functions with which to expand such perturbations. For the open Robertson Walker cosmology, this question will be completely answered. In addition, some observations will be made concerning explicit solution by separation of variables of wave equations for spin s in a Riemannan space having an infinitesmal line element of which the Robertson Walker models are a special case.

Complete sets of functions for perturbations of Robertson–Walker cosmologies and spin 1 equations in Robertson–Walker-type space-times

Crucial to a knowledge of the perturbations of Robertson–Walker cosmological models are complete sets of functions with which to expand such perturbations. For the open Robertson–Walker cosmology an answer to this question is given. In addition some observations concerning explicit solution by separation of variables of wave equations for spin 1 in a Riemannian space having an infinitesimal line element of which the Robertson–Walker models are a special case are made.

«4 + 6»-Decomposition of ten-dimensional octonionic spinor wave equations and derivation of four-dimensional massless Dirac equations

A method of decomposition into external four dimensions and internal six dimensions of the wave equations of octonionic spinors in ten dimensions is given. To obtain the spinor wave equations in the external four-dimensional Minkowski space-time, octonions in the extra internal six dimensions are described. The zero-mode solutions of the extra six-dimensional octonionic wave equations are also argued, and the Dirac equations in the four-dimensional Minkowski space-time are derived. Moreover, we investigate a possibility of the chiral asymmetric fermions in four dimensions.

Symmetry operators and separation of variables for spin-wave equations in oblate spheroidal coordinates

A family of second-order differential operators that characterize the solution of the massless spin s field equations, obtained via separation of variables in oblate spheroidal coordinates and using a null tetrad is found. The first two members of the family also characterize the separable solutions in the Kerr space-time. It is also shown that these operators are symmetry operators of the field equations in empty space-times whenever the space-time admits a second-order Killing–Yano tensor.

Spin-wave instabilities, auto-oscillations, and chaos in yttrium-iron-garnet

A review is presented of recent experimental results in yttrium-iron-garnet subject to three different spin-wave pumping mechanisms: parallel pumping, subsidiary resonance (first-order Suhl process), and premature saturation of the main resonance (second-order Suhl process). A theoretical model derived from first principles and leading to coupled nonlinear spin-wave equations, is used to interpret the observed spin-wave instabilities, auto-oscillations, and chaotic dynamics. It is shown that a two-mode model explains the main features of the experimental observations, both in parallel and perpendicular pumping. Improvements needed in the model are indicated. >

A particle mechanics description of antisymmetric tensor fields

In a previous work the authors discussed the action for a massless relativistic point particle with a gauged N-extended worldline supersymmetry that yields, upon quantisation, a relativistic wave equation for pure spin N/2. They present further details, emphasising the N=2 particle model for which a wavefunction with O(2) charge q can be interpreted as the field strength of a (q-1)-form gauge potential. They present extensions of this model that yield field equations for massless and massive antisymmetric tensors in arbitrary spacetime dimension d. They show how to obtain chirality and generalised self-duality conditions.

Wave equations for arbitrary spin from quantization of the extended supersymmetric spinning particle

We present the action for a relativistic particle with a gauged N-extended line supersymmetry and show that, upon quantization, it yields a relativistic wave equation for pure spin 1 2 N . A curved-space background is compatible with worldline supersymmetry only for N⩽2.

Spinor fields and the GL(4,R) gauge structure in the nonsymmetric theory of gravitation

The spinor structure associated with the local gauge group GL(4,R) of the nonsymmetric gravitation theory (NGT) is based on a spinor wave equation constructed from a vierbein, a GL(4,R) spin connection, and the infinite-dimensional irreducible representations of the universal covering group 𝒮ℒ (4,R) of the noncompact group SL(4,R). The multiplicity-free irreducible representations of 𝒮ℒ (4,R) correspond to bivalued spinorial representations of SL(4,R) that contain an infinite number of half-odd integer spin particles. By adjoining the translations T4, the extended group 𝒜=T4×GL(4,R) replaces the Poincaré group 𝒫. The properties of the mass spectrum are obtained from an infinite-component wave equation and the physical spinor field consists of an infinite sum of finite, nonunitary representations of the Lorentz group.

On Huygens' Principle for the Relativistic Higher Spin Wave Equations of Buchdahl and Wünsch in Presence of a Gravitational and an Electromagnetic Field

A field of spin s (s ≧ 1/2) massive particles can be described in an arbitrarily curved space-time by a system of first order equations introduced by H. A. Buchdahl [2] and V. Wünsch [13]. In this paper we generalize this system by minimal coupling of an electromagnetic field. The arising first order system implies a second order differential equation of normal hyperbolic type on which the usual techniques can be applied. It is shown here that the field equations satisfy Huygens' principle if and only if the space-time has constant curvature and the electromagnetic field vanishes.

Spinor focus wave modes

New solutions of the homogeneous spinor wave equation are obtained. They are similar to the focus wave mode solutions of Maxwell’s equations leading to a Gaussian pulse energy. A weighted superposition of these modes may supply finite energy pulses. The particular case of Bessel weight functions is discussed.

Separability of the Killing–Maxwell system underlying the generalized angular momentum constant in the Kerr–Newman black hole metrics

The concept of a Killing–Maxwell system may be defined by the relation Â[μ;v];ρ =(4π/3)ĵ[μgν]. In such a system the one-form Âμ is interpretable as the four-potential of an electromagnetic field F̂μv, whose source current ĵ μ is an ordinary Killing vector. Such a system determines a canonically associated duality class of source-free electromagnetic fields, its own dual being a Killing–Yano tensor, such as was found by Penrose [Ann. N.Y. Acad. Sci. 224, 125 (1973)] (with Floyd) to underlie the generalized angular momentum conservation law in the Kerr black hole metrics, the existence of the Killing–Yano tensor being also a sufficient condition for that of the Killing–Maxwell system. In the Kerr pure vacuum metric and more generally in the Kerr–Newman metrics for which a member of the associated family of source-free fields is coupled in gravitationally, it is shown that the gauge of the Killing–Maxwell one-form may be chosen so that it is expressible (in the standard Boyer–Lindquist coordinates) by 1/2 (a2 cos 2 θ−r2)dt+ 1/2 a(r2−a2)sin2 θ dφ, the corresponding source current being just (4π/3)(∂/∂t). It is found that this one-form (like that of the standard four-potential for the associated source-free field) satisfies the special requirement for separability of the corresponding coupled charged (scalar or Dirac spinor) wave equations.

Intrinsic nonlinear spinor wave equations associated with nonlinear spinor representations

New covariant nonlinear spinor wave equations associated with nonlinear spinor representations of pseudo-orthogonal groups are derived. The wave equations obtained possess specific nonlinearities, which, in the intrinsic spinor coordinates, have the form of bilinear nonlinearities. Due to the existence of a large number of natural constraints, typical for nonlinear spinor representations, the number of independent spinor components in the present theory is considerably reduced.

Second-order wave equation for spin-1/2 fields. II. The Hilbert space of the states.

It is shown that, for spin-1/2 fields ruled by a second-order wave equation, it is possible to define a conserved current density whose zero component is positive definite. Hence one can (1) give a coherent statistical interpretation of the wave function, and (2) define a Hilbert space of the states with all the usual quantum-mechanical formalism. A new linearized form of the wave equation, completely equivalent to the second-order one, is finally presented.

Propagation of electromagnetic plane waves in random media

In the frame of the spinor formalism of the electromagnetic field, the propagation of a plane wave in a random medium with a view to obtaining the moments of the energy density is considered. Using two different approximations to the solution of the spinor wave equation, it is shown that the energy conservation requires, on the statistics of the refractive index, some extra conditions difficult (eventually impossible) to satisfy. For the variance of the light intensity, a result valid for weakly scattering media is given. It is concluded that ‘‘dishonest’’ methods (in Keller’s terminology) have to be used.

Second-order wave equation for spin-(1/2) fields.

Some features of the second-order Feynman--Gell-Mann wave equation are discussed in order to show that (1) a statistical interpretation in terms of particles and antiparticles is possible, (2) the Dirac condition must be considered too restrictive, (3) no unwanted results arise from the use of this equation.

Cauchy's problem and Huygens' principle for relativistic higher spin wave equations in an arbitrary curved space-time

Relativistic spins (s >/ 1/2), nonzero mass equations are given which in an arbitrary curved space-time are internally consistent. By means of Riesz' integration method a representation theorem for the solution of Cauchy's problem, using the constraints of the Cauchy data on the initial hypersurface and suitable “Green's formulas,” is proved. Finally, a necessary and sufficient condition for the validity of Huygens' principle is stated from which it follows that only in space-times of constant curvature do the field equations satisfy Huygens' principle.

Approximate causal solutions for a class of wave equations with backscatter

The construction of solutions of wave equations with backscatter usually requires the use of some kind of approximation scheme. A problem then arises—how can one ensure that the approximate solution is causal? In this paper we present a method of constructing approximte causal wave-zone solutions that is applicable to a class of wave equation which reduce in form, in the limit as an expansion parameter goes to zero, to the scalar wave equation in flat space-time expressed in terms of the null coordinate u0=t−r. An extension of the method which is applicable to higher spin wave equations is also given.

Pauli-Fierz and Rarita-Schwinger wave equations and their equivalence

It is show that the Pauli-Fierz wave equation for spin 3/2 is equivalent to the Rarita-Schwinger wave equation and hence both violate causality when minimally coupled to an external electromagnetic field.

Textures and spin waves in rotating superfluid3H3-B

The spin wave modes in rotating superfluid3He-B have been calculated for a texture of cylindrical symmetry. The textural configuration is determined by minimizing the appropriate free energy and solving the resulting Euler-Lagrange equations for then vector. The texture determines the effective potential entering the spin wave equation. The potential deviates significantly from a harmonic oscillator under realistic experimental conditions, giving rise to shifts of the oscillator frequencies. The agreement with the recent experimental observations of Ikkalaet al. is excellent at all temperatures studied.

On the Shamaly-Capri wave equation for spin-1 particles

The equivalence of the Shamaly-Capri wave equation to the Gel’fand-Yaglom wave equation for spin 1 is verified and is shown that there are difficulties with the charge which reflect on its causal propagation.