Covariant Equations Research Articles

A Novel Interpretation of the Klein-Gordon Equation

The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an initial boundary condition, this paper considers the possibility that the solutions are determined by both an initial and a final boundary condition. By constructing an invariant joint probability distribution from the size of the solution space, it is shown that the usual measurement probabilities can nearly be recovered in the non-relativistic limit, provided that neither boundary constrains the energy to a precision near hbar/T (where T is the time duration between the boundary conditions). Otherwise, deviations from standard quantum mechanics are predicted.

Charged Dirac particles’ Hawking radiation via tunneling from the general non-extremal rotating charged black hole of D=5 minimal gauged supergravity

Motivated by Kerner and Man’s fermions tunneling method of dimension 4 black holes, in this paper, we further improve the analysis to investigate Hawking radiation of charged Dirac particles with spin 1/2 from general non-extremal rotating charged black holes with two parameters and a non-zero cosmological constant in minimal five-dimensional gauged supergravity. For space-times with different horizon topology and different dimensions, constructing a set of appropriate γμ matrices for general covariant Dirac equation is an important technique for the fermion tunneling method. By introducing a set of appropriate matrices γμ and employing the ansatz for the spin-up spinor field, we successfully recovered the tunneling probability of charged Dirac particles and the expected Hawking temperature of the black hole, which is exactly consistent with that obtained by other methods. Moreover, the fermion tunneling method can be directly applied to the other five-dimensional charged black holes, which strengthens the validity and power of the fermion tunneling method.

Hawking temperature from the charged Kerr black hole in five dimension via fermions tunneling method

In this paper, motivated by fermions tunneling method of 4 dimensional black holes, we extend the analysis to the charged Kerr black hole in five dimension by constructing a set of appropriate matrices γμ for general covariant Dirac equation. As a result, we successfully recover the expected Hawking temperature.

On the Poincaré Gauge Theory of Gravitation

We present a compact, self-contained review of the conventional gauge theoretical approach to gravitation based on the local Poincaré group of symmetry transformations. The covariant field equations, Bianchi identities and conservation laws for angular momentum and energy-momentum are obtained.

Octonion wave equation and tachyon electrodynamics

The octonion wave equation is discussed to formulate the localization spaces for subluminal and superluminal particles. Accordingly, tachyon electrodynamics is established to obtain a consistent and manifestly covariant equation for superluminal electromagnetic fields. It is shown that the true localization space for bradyons (subluminal particles) is R 4- (three space and one time dimensions) space while that for the description of tachyons is T 4- (three time and one space dimensions) space.

Hydrodynamic Lagrangian of relativistic superfluids with crystalline structure

We propose a relativistic Lagrangian formulation of macroscopic dynamics of superfluid systems. The constructed Lagrangian provides the description of ordinary superfluids and superfluids with a crystalline ordering, where both phase and translational symmetries are simultaneously broken (e.g., supersolids or crystalline superfluids in neutron stars). The covariant conservation laws and equations of motion for the field variables associated with the broken symmetries are obtained. The connection to Khalatnikov–Lebedev relativistic hydrodynamic theory is discussed.

How to obtain the covariant form of Maxwell's equations from the continuity equation

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

Hawking radiation of Dirac particles from Kerr–AdS black hole in five dimensions

By constructing a set of appropriate matrices γμ for general covariant Dirac equation, we further extend fermion tunneling method to 5-dimensional Kerr–AdS black hole, and show that the expected Hawking temperature is recovered.

Covariant formulations of Baumgarte, Shapiro, Shibata, and Nakamura and the standard gauge

The Baumgarte-Shapiro-Shibata-Nakamura (BSSN) and standard gauge equations are written in covariant form with respect to spatial coordinate transformations. The BSSN variables are defined as tensors with no density weights. This allows us to evolve a given set of initial data using two different coordinate systems and to relate the results using the familiar tensor transformation rules. Two variants of the covariant equations are considered. These differ from one another in the way that the determinant of the conformal metric is evolved.

A canonical relativistic approach to quantize electromagnetic field in the presence of moving magneto-dielectric media

A canonical relativistic formulation is introduced to quantize electromagnetic field in the presence of a polarizable and magnetizable moving medium. The medium is modeled by a continuum of four vectors in a phenomenological way. The covariant wave equation for the vector potential and the covariant constitutive equation of the medium are obtained as the Euler- Lagrange equations using the Lagrangian of the total system. A tensor of the third rank which couples the electromagnetic field with the medium is introduced and the susceptibility tensor of the medium is obtained in terms of the coupling tensor. Also the noise polarization tensor is calculated in terms of the coupling tensor and the creation and annihilation operators of the four vectors modeling the medium.

Survey of Nucleon Electromagnetic Form Factors

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincare' covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensurate with the pion's charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are: r_1^{n,u}>r_1^{n,d}, owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.

Rotating light, the orbital angular momentum paradox and relativistic complex scalar fields

Recent studies show that the angular momentum, both spin and orbital, of rotating light beams possesses counter-intuitive characteristics. We present a new approach to the question of the orbital angular momentum of light based on the complex massless scalar field representation of light. The covariant equation for the scalar field is treated in a rotating system using the general relativistic framework. The equivalence of the U(1) gauge current for the scalar field with the Poynting vector continuity equation for paraxial light is used to apply the formalism to the calculation of the orbital angular momentum of rotating light beams. If the difference between the co-, contra- and physical quantities is properly accounted for there is no paradox in the orbital angular momentum of rotating light. An artificial analogue of the paradoxical situation could be constructed but it is wrong within the present formalism. It is shown that the orbital angular momentum of a rotating beam comprising modes with opposite azimuthal indices corresponds to that of rigid rotation. A plausible physical explanation of this feature is suggested in analogy with the rigid rotation of the vortex core in a rotating fluid.

Quantum vortices of type II superconductors in curved space-time and Cattaneo’s projection method

In this paper we show that the covariant dynamical equations of quantum vortices in type II superconductors may be brought into the same form as the classical equations written in 3-vector forms and can then be interpreted by using the familiar language of physics. This result is attained by introducing the physically measurable quantities by means of the corresponding standard relative quantities as defined by Cattaneo and by using his operator of transverse derivation, partial or covariant, with respect to the ${x}^{4}$ lines. The standard equations thus obtained have a tensorial character and are covariant under the sole changes of coordinates leaving invariant the ${x}^{4}$ lines, i.e. changes of coordinates internal to the physical system of reference S associated with the coordinates (${x}^{i}$). Expressions of the electric and magnetic fields induced inside a type II superconductor at rest in a curved space-time are obtained. The generation of these fields is influenced not only by the presence of a gravitational field but also by the presence of vortices. Comparison is made with the results predicted by the method of anholonomic frames.

Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.

Toward unifying the description of meson and baryon properties

A Poincare' covariant Faddeev equation is presented, which enables the simultaneous prediction of meson and baryon observables using the leading-order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleon's dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic Q^2-evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with r_1^{nu}>r_1^{nd}. The proton electric-magnetic form factor ratio falls with increasing Q^2.

Tunneling of Dirac Particles from a Double Myers-Perry Black Hole in Five Dimensions

Motivated by the fermions tunneling formalism of Kerner and Mann, we attempt to investigate quantum tunneling of Dirac particles from a five dimensions double Myers-Perry black hole, which describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter and both in the same plane. After introducing several appropriate Gamma matrixes for the covariant Dirac equation, we obtain the tunneling probability of Dirac particles from the double Myers-Perry black hole, which gives the expected emission temperature as the case of scalar particles that obtained by others.

Fermions tunneling from apparent horizon of FRW universe

In the paper [R.-G. Cai, L.-M. Cao, Y.-P. Hu, arXiv: 0809.1554], the scalar particles' Hawking radiation from the apparent horizon of Friedmann–Robertson–Walker (FRW) universe was investigated by using the tunneling formalism. They obtained the Hawking temperature associated with the apparent horizon, which was extensively applied in investigating the relationship between the first law of thermodynamics and Friedmann equations. In this Letter, we calculate fermions' Hawking radiation from the apparent horizon of FRW universe via tunneling formalism. Applying WKB approximation to the general covariant Dirac equation in FRW spacetime background, the radiation spectrum and Hawking temperature of apparent horizon are correctly recovered, which supports the arguments presented in the paper [R.-G. Cai, L.-M. Cao, Y.-P. Hu, arXiv: 0809.1554].

ABELIAN MAGNETIC MONOPOLES AND TOPOLOGICALLY MASSIVE VECTOR BOSONS IN SCALAR-TENSOR GRAVITY WITH TORSION POTENTIAL

A Lagrangian formulation describing the electromagnetic interaction — mediated by topologically massive vector bosons — between charged, spin-½ fermions with an Abelian magnetic monopole in a curved space–time with nonminimal coupling and torsion potential is presented. The covariant field equations are obtained. The issue of coexistence of massive photons and magnetic monopoles is addressed in the present framework. It is found that despite the topological nature of photon mass generation in curved space–time with isotropic dilaton field, the classical field theory describing the nonrelativistic electromagnetic interaction between a point-like electric charge and magnetic monopole is inconsistent.

Besov Spaces and Self-Similar Solutions for the Wave-Map Equation

Self-similar solutions play a crucial role in the blow-up theory for the wave-map equation; they correspond to self-similar data at the time of the blow-up. However, solutions to this equation are generally considered for data in the standard finite energy spaces (in dimension d) . We build up in this article solutions of the covariant wave-map equation for data which are small and of infinite energy, or large and self-similar. This provides us with a general framework which includes in particular the blowing up solutions of Shatah [14] and Bizoń [3]. As an application, we describe more precisely the blow-up phenomenon.

An effective metric for interactions of laser field with plasma

The interactions of laser field with plasma are studied by using the analog model of gravity. The interactions of laser field with plasma are regarded as an equivalent effective geometry. An effective metric for a plasma electron is developed. Validity of the metric is confirmed in the limit of non-relativity. The three-dimensional equation of motion for a plasma electron is derived from the general covariant equation of motion. The ponderomotive force and the Abraham’s force are directly obtained from the three-dimensional equation.