Vacuum Wave Research Articles

Fourth-order calculation of the vacuum wave function and mass gap of SU(2) lattice gauge theory in 2+1 dimensions.

The long wavelength vacuum wave function and mass gap of SU(2) lattice gauge theory in 2+1 dimensions are calculated by a truncated eigenvalue equation method. The mass gap shows good scaling behavior at both third and fourth order.

Variational Approximation of Density Matrix on the Basis of Ground State: Thermalization of Vacuum

We formulate the Feynman's variational principle for a density matrix by means of Bohm-Madelung representation using Lagrange variables, which appear to be dynamical invariants of phase flux with sources on the ends of trajectories. With a linear parametrization in invariants for the flux the variational problem can be formulated as the extended principle of least action in which the functional variables appear to be trajectories of the center and the dispersion of the renormalized vacuum wave packet, which is reduced at the ends of the trajectories. Approximating the extended action in terms of bilocal frequency, we derive an explicit expression which provides the exact result for the linear systems and, in general case, proper semi-classical correction and correct asymptotics for the ground state. We examine the effect of spontaneous symmetry breaking on the coordinate distribution as well.

Weak gravitation waves in vacuum and in media: Taking nonlinearity into account.

Weak gravitation waves in vacuum and in media: Taking nonlinearity into account.

THE WAVE EQUATIONS FOR THE LANCZOS TENSOR/SPINOR, AND A NEW TENSOR IDENTITY

The apparent discrepancy between the vacuum wave equations obtained for the Lanczos potential respectively by spinor and tensor methods is explained; it is shown that the additional expression in the tensor version is actually identically zero in four dimensions.

An electromagnetic wave approach to matter and radiation

In this paper, we propose a new approach concerning the existence and propagation of matter and radiation in vacuum. By considering the possible existence of scalar inhomogeneous standing waves in vacuum, we were able to derive Maxwell's equations and Lorentz force laws from first principles.

Analytic calculation of the vacuum wave function for (2+1)-dimensional SU(2) lattice gauge theory.

The long wavelength vacuum wave function of (2+1)-dimensional SU(2) lattice gauge theory is calculated by the method of truncated eigenvalue equation. Third order results are consistent with Monte Carlo measurement and display a good scaling behavior extending to the deep weak coupling region.

Transformation of X-Ray polarization under dynamical grazing incidence diffraction

The transformation of the X-ray polarization under grazing incidence diffraction is studied. The dependencies of the parameters of the polarization ellipses for specularly reflected and diffracted waves in vacuum on the corresponding parameters of the incident wave with arbitrary polarization are found. Strong spatial crystal anisotropy close to the exact Bragg condition and the existence of two critical reflection angles manifest themselves in a steep change of the polarization state of the secondary waves near these points. It is shown that diffraction conditions exist such that an incident linearly polarized beam of X-ray quanta can acquire a high degree of circular polarization during the reflection process. [Russian Text Ignored].

Sagnac experiment with electrons: Observation of the rotational phase shift of electron waves in vacuum.

A Sagnac experiment with electron waves in vacuum is reported. The phase shift caused by rotation of an electron biprism interferometer placed on a turntable has been measured. It was found to agree with prediction within error margins of about 30%. A compact ruggedized electron interferometer was used. It is based on a high-precision optical bench of 36-cm length. This interferometer is less sensitive by orders of magnitude to mechanical vibrations and electromagnetic stray fields than conventional electron interferometers. A beam of low-energy electrons (150\char21{}3000 eV) emitted by a field-emission electron source was used. For the most part, electrostatic electron optical components were employed. The magnified interference fringe pattern was intensified by a dual-stage multichannel-plate intensifier, recorded by a charge-coupled-device video camera, transmitted from the turntable to the laboratory system via a slip ring, and evaluated by an image-processing system. Both the rotation rate and the area enclosed between the two partial waves were varied (up to values of 0.5 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and 3.9 ${\mathrm{mm}}^{2}$, respectively). Fringe shifts on the order of 5% of a fringe period were attained. Some historical aspects of the Sagnac effect as well as some aspects of its interpretation are mentioned. A brief informal discussion is included of the interpretation of the Sagnac phase shift as a geometric phase (``Berry phase'') caused by the global anholonomy of the local phase factor that is produced by the gauge field induced by rotation.

Particle dynamics in spherical wave fields of rotating magnets - Acceleration boundary, plasma border, and 1/r(0)-squared law of asymptotic energy

view Abstract Citations (3) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Particle Dynamics in Spherical Wave Fields of Rotating Magnets: Acceleration Boundary, Plasma Border, and 1/r 2 0 Law of Asymptotic Energy Thielheim, K. O. Abstract Spherical wave fields generated by rotating stellar magnets can be powerful cosmic particle accelerators, some characteristics of which are described in the present paper. On a first stage particle dynamics is studied for vacuum wave fields. Among the features discussed here are the acceleration boundary, which is related to the decoupling of a particle from a spherical wave field and the plasma border, which is related to the reflection of particles by a spherical wave, field. Also, the asymptotic energy of particles originating from the range between the acceleration boundary and the plasma border or reflected by the spherical wave field is considered. Then, on a second stage, particle dynamics is discussed for plasma wave fields. Specifically, the survival of the acceleration boundary is investigated in terms of the typical phase velocity and the typical particle flux as well as the development of particle energy in spherical wave fields. Publication: The Astrophysical Journal Pub Date: May 1993 DOI: 10.1086/172667 Bibcode: 1993ApJ...409..333T Keywords: Dynamo Theory; Particle Accelerators; Plasma Waves; Stellar Magnetic Fields; Cartesian Coordinates; Equations Of Motion; Plane Waves; Spherical Coordinates; Plasma Physics; ACCELERATION OF PARTICLES; MAGNETOHYDRODYNAMICS: MHD; PLASMAS full text sources ADS |

Gravity waves in vacuum and in media: the wave equation, the role of nonlinearity, the stress-energy tensor and the low-frequency cut-off

The gravity waves stress-energy tensor in arbitrary media, on an arbitrary curved background, is derived and studied. The natural low-frequency cut-off is introduced and is shown to depend on the peculiarities of the observer only. The wave equation for weak gravity oscillations is written down with two nonlinear next-after-leading-order terms. The role of nonlinearity is discussed.

Monte Carlo measurement of the vacuum wave function in non-abelian gauge theory

The vacuum wave function is investigated by Monte Carlo simulation for SU(2) lattice gauge theory in D=3 dimensions. The vacuum wave function obtained on the lattice is expanded in terms of the lattice spacing and the scaling behavior is observed for the coefficients not only of the field strength squared but also of its covariant derivative squared. The result implies that the correlation length in the vacuum has the same order of magnitude as the confinement scale.

Mean field solution of QCD 2 in the large- N limit

Two-dimensional QCD in the large- N limit is formulated as a Hartree-Fock problem and solved numerically on a lattice. Calculation of single-particle wave functions and the one-body density matrix displays the structure of baryons. Insight into the Skyrme model is provided by showing that in the limit of small quark mass, the baryon is accurately approximated by a spatially varying chiral rotation of the vacuum wave function, where the chiral angle satisfies the sine-Gordon equation. The meson spectrum is calculated in the random phase approximation. The same mean field theory is also applied to chiral and non-chiral Gross-Neveu models, where it agrees with known analytical results.

Continuum limit of exactly solvable Hamiltonian in lattice gauge theory.

We investigate the modified lattice gauge Hamiltonian proposed by Guo, Zheng, and Liu, whose vacuum wave function is known exactly. The result strongly suggests that the Hamiltonian does not have the correct continuum limit in either (2+1)-dimensional or (3+1)-dimensional space-time. We also show that the modified Hamiltonian cannot be improved so as to make its difference from the standard Kogut-Susskind Hamiltonian negligible in the continuum limit under the condition that its exact vacuum wave function is the product of the functions of a single plaquette variable.

The ionosphere as an Alfven resonator in the Pc1 micropulsation range

A local planar approximation of a stratified, inhomogeneous, anisotropic and dissipative ionosphere is presented as an Alfven quarter-wave plate resonator in the Pc1 micropulsation range. The frequency-amplitude structure of the resonance response of an isotropic Alfven wave on the Earth's surface and at a given altitude in the ionosphere is studied in comparison to standing waves in vacuum above an ideal conductor for a particular model of the ionosphere. An asymmetry in the response was found at both boundary of the resonator, at the Earth's surface and at the given altitude z0. The results are related to the vertical changes of frequency dispersion in the dissipative medium of the ionosphere and to the vertical profile of the inhomogeneities of the resonator being considered.

On the gravitational interaction of null fields

The authors show that when two null fields with planar symmetry collide, they generate a source which behaves as a non-perfect fluid, and that an infinite energy density always develops at a finite time after the instant of collision. Since the Klein-Gordon equation for a massless scalar field is satisfied in the region of interaction, and since the scalar field satisfies the required junction conditions across the null boundaries, the null colliding fields can be interpreted as scalar waves. The four-parameter family of solutions of the Einstein equations they present also includes most of the known solutions for the collision of gravitational plane waves in vacuum, or coupled with stiff matter.

The gravitational faraday rotation for cylindrical gravitational solitons

By using cylindrical soliton solutions, the nonlinear behavior of gravitational waves in vacuum is studied in terms of a rotation of the polarization vector between two independent modes. This effect was emphasized by Piran, Safier, and Stark as a gravitational analogue of the Faraday rotation. The polarization of the soliton wave is calculated, and it is found that the+mode which was dominant near the axis of symmetry is fully converted to the×mode at some interaction region and then the disturbance propagating along a light cone like a gravitational wave pulse contains both polarizations.

Impossibility of centrally symmetric shock waves in vacuum in the relativistic theory of gravitation

Impossibility of centrally symmetric shock waves in vacuum in the relativistic theory of gravitation

Nonprojectiveness of Moiré Fringe Patterns Observed in X-Ray Diffraction

Interference fringes in X-ray diffraction must be a projected figure thrown to the wave-traveling direction, due to the property of the wave field that Δ K =const. along the wave path and Δ K ⊥\bar K ( Δ K = K '- K and \({\bar{\mbi{K}}}{=}{\frac{1}{2}}(\mbi{K}{+}\mbi{K}'\)), K and K ' being the wave vectors of interfering waves in vacuum). The second property comes from the condition | K |=| K '|. The question of whether moiré fringes have this projective property was examined experimentally. Moiré fringes were observed from a monolithic Si bicrystal by X-ray topography. Experiments have shown that the directions and positions of moiré fringes vary with the shift of the observation point along the wave path in oscillatory manners, and thus the moiré fringes are not exactly the projected figure. This fact indicates that the first or both of the conditions, Δ K =const. and Δ K ⊥\bar K , do not apparently hold in the moiré-fringe interference.

Nonperturbative treatment of the functional Schrödinger equation in QCD.

Use of the functional Schroedinger equation in QCD is complicated by the need to maintain gauge invariance at the same time one is dealing with nonperturbative effects (at least at long distances). Moreover, asymptotic freedom must be recovered at short distances. In this paper we show how to set up and solve a set of Ward identities which ensure gauge invariance of the wave functional, which can then be parametrized simply and used with various nonperturbative algorithms (e.g., variational). Parametrizations are found both for the vacuum wave functional and for J/sup P//sup C/ = 0/sup +- //sup +/ quantum soliton states of QCD. A nonperturbative algorithm, based on the observation that a wave functional is really a partition function in the presence of a special kind of source, is set up and applied; this algorithm is based on dressed-loop expansions of partition functions. One recovers this way some earlier results found from the study of Schwinger-Dyson equations, plus some new results concerning the 0/sup -+/ soliton, whose wave functional involves the Chern-Simons secondary class function.

Radiation pressure and lateral forces on a moving conductor sheet

Abstract The paper deals with the effect of the radiation pressure and lateral forces on a moving conductor sheet, whose speed is parallel to the normal vector of the sheet; these forces become significantly large when the sheet speed approaches the velocity of a plane electromagnetic wave in vacuum, independently of the sense of movement (sheet moving ‘away’ from the beam or ‘meeting’ the beam). Significant graphical results are presented.