Tachyonic γ-ray bursts generated by nonlocal plasma currents

The dispersion relations of superluminal wave propagation in electron plasmas are derived, and the tachyonic energy flux, the velocity of energy transport, and the relaxation time asymptotics of the conductivity are studied. The formalism is based on Maxwell-type equations for Proca fields with negative mass-square in dispersive and dissipative media. Specifically, superluminal radiation fields generated by the ultra-relativistic electronic source plasma of γ-ray bursts (GRBs) are investigated. The radiation field is coupled to the shock-heated electron gas by a frequency-dependent fine-structure constant. The varying coupling constant generates long-range dispersion in the charge and current densities. At high energy, the coupling strength approaches a finite limit, so that the Proca field becomes minimally coupled to the electron current. The tachyonic fine-structure constant scales with the frequency-dependent superluminal velocity of the radiated modes. This scaling is manifested in the tachyonic flux densities of the GRB plasma, so that the scaling exponent can be extracted from spectral maps in the soft γ-ray band. To this end, tachyonic spectral fits of GRB 930506, GRB 950425, and GRB 910503 are performed. The scaling amplitude of the fine-structure constant is inferred from the burst duration. The transversal and longitudinal tachyonic luminosity of the source plasma is calculated in the high-temperature regime. Estimates of the plasma temperature and the internal energy of the ultra-relativistic electron gas are obtained.     

Proca fields interpretation of spin 1 equation in Robertson-Walker space-time

The general scheme for massive spin 1 equation in curved space-time is specialized to describe the Proca fields. The expressions of the Proca tensor fields are detailed in the Robertson-Walker space-time by means of the solutions of the spin 1 equation in a given tetrad and by the components of the tetrad itself. Asymptotic behaviours of the fields are discussed in the flat, closed and open space-time cases.Also GNFM, Italy     

Field Equations of Arbitrary Spin in Space-time with Torsion

A two spinor lagrangian formulation of field equations for massive particle of arbitrary spin is proposed in a curved space-time with torsion. The interaction between fields and torsion is expressed by generalizing the situation of the Dirac equation. The resulting field equations are different (except for the spin-1/2 case) from those obtained by promoting the covariant derivatives of the torsion free equations to include torsion. The non linearity of the equations, that is induced by torsion, can be interpreted as a self-interaction of the particle. The spin-1 and spin-3/2 cases are studied with some details by translating into tensor form. There result the Proca and Rarita-Schwinger field equations with torsion, respectively. PACS numbers: 03.65.Pm; 04.20.Cv; 04.20.Fy.     

Static and quasistatic solutions of the real Proca field

We consider the theory of the massive real vector field with spin 1 (the real Proca field) and its solutions. First the field equations with dual symmetry [1] are written and the 4-pseudo vector is chosen to be zero. The constants of motion for the real Proca field, the constant “electric” real Proca field, the uniform motion of a point charge in the real Proca field, uniform motions in the “Coulomb” field, dipole and multipole free-momentum, constant “magnetic” field, and the field of a point charge in motion are presented.     

Generalized Klein–Gordon field equations with octonion space-time (OST) algebra

The concept of space-time representation is redefined using the octonion space-time (OST) algebra. In this study, describing the properties of octonions and their possible connection with Euclidean space-times, the internal and external space-time events are represented within the OST algebra. Keeping in mind the octonionic dual-Euclidean space-times, we express the homogeneous field equations which leads to the symmetrical nature of internal and external space-times. We derive the generalized Proca–Maxwell equations for massive-dyons in the case of the OST algebra. Accordingly, we have obtained a new set of octonionic Klein–Gordon potential (KGP) and Klein–Gordon field (KGF) equations for massive dyons from the generalized Proca–Maxwell equations. This formalism demonstrates that the octonionic KGP and KGF equations can be expressed in a single equation and it is equivalent to energy-momentum relation for dyons. As such, we have made an attempt to write the conservation of Noetherian current from the octonionic Klein–Gordon equations.     

Proca Effects of Axion-Like Particle-Photon Interactions on Light Polarization in External Magnetic Fields

Photon can mix with the axion-like particles (ALPs) on light polarization when the laser beam travels through a magnetic field. Since there is no conclusive evidence of an exact zero rest mass for the photon in various experiments and observations, we study the Proca effects in various ALP-photon regeneration experiments and develop a formalism which can be adopted to study the evolution of a massive photon in the presence of external magnetic fields. We find that the Proca effects are much smaller than the effects of the standard QCD axions. But if the masses of such particles are comparable, the Proca effects can not be neglected. Furthermore, we get the implied photon mass limit and discuss the feasibility of extending the search for the photon mass limit in this area.     

A linear relativistic model of processes with causal faster-than-light effects

To get a synthesis of causal faster-than-light effects and signals that do not propagate faster than light by using local, covariant, linear equations of motion, we propose the following hypothesis. Free fields that propagate signals according to the Klein-Gordon, Dirac, Proca or Maxwell equations, are actually describing only smoothed-out, average properties of underlying causal transport processes of point like entities with arbitrary four-momenta, the states of which are described by a scalar, spinor or four-vector field that satisfies a local, covariant, linear transport equation. An example of such a linear, causal, covariant transport process is shown to display causal faster-than-light effects, to propagate signals not faster than light, and to contain the Klein-Gordon equation as a limiting case. An analogous transport model displays causal, four-vector, faster-than-light effects, and also distinctive four-vector, long-range and short-range effects that do not propagate faster than light.     

Evolution Equation for a Joint Tomographic Probability Distribution of Spin-1 Particles

The nine-component positive vector optical tomographic probability portrait of quantum state of spin-1 particles containing full spatial and spin information about the state without redundancy is constructed. Also the suggested approach is expanded to symplectic tomography representation and to representations with quasidistributions like Wigner function, Husimi Q?function, and Glauber-Sudarshan P?function. The evolution equations for constructed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are found. The evolution equations are also obtained in special case of the quantum system of charged spin-1 particle in arbitrary electro-magnetic field, which are analogs of non-relativistic Proca equation in appropriate representations. The generalization of proposed approach to the cases of arbitrary spin is discussed. The possibility of formulation of quantum mechanics of the systems with spins in terms of joint probability distributions without the use of wave functions or density matrices is explicitly demonstrated.     

Vector bosons in the expanding universe

We exactly solve the relativistic wave equation for vector bosons in the expanding universe and show that the current of the vector bosons in this background is rapidly oscillating in early time. Additionally, we derive the solutions of the Proca equation from the solutions of the Duffin-Kemmer-Petiau (DKP) equations in the same background and obtain the massless-particle, photon, solutions by taking the limit of these solutions. PACS. 03.65.Pm, 04.60.-m, 98.80.Cq Received: 20 May 2005, Published online: 30 August 2005     

Einstein-Proca Model, Micro Black Holes, and Naked Singularities

The Einstein-Proca equations, describing a spin-1 massive vector field in general relativity, are studied in the static spherically-symmetric case. The Proca field equation is a highly nonlinear wave equation, but can be solved to good accuracy in perturbation theory, which should be very accurate for a wide range of mass scales. The resulting first order metric reduces to the Reissner-Nordström solution in the limit as the range parameter goes to zero. The additional terms in the g ₀₀ metric coefficient are positive, as in Reissner-Nordström, in agreement with previous numerical solutions, and hence involve naked singularities.     

Analysis of the wave functions for accelerating Kerr-Newman metric

As is well-known, it is very difficult to solve wave equations in curved space-time. In this paper,we find that wave equations describing massless fields of the spins s≤2 in accelerating KerrNewman black holes can be written as a compact master equation. The master equation can be separated to radial and angular equations, and both can be transformed to Heun's equation,which shows that there are analytic solutions for all the wave equations of massless spin fields.The results not only demonstrate that it is possible to study the similarity between waves of gravitational and other massless spin fields, but also it can deal with other astrophysical applications, such as quasinormal modes, scattering, stability, etc. In addition, we also derive approximate solutions of the radial equation.     

实验检验光子静止质量的研究进展

爱因斯坦狭义相对论的基本假设之一是光速不变性,其直接推论就是光子的静止质量必须为零,因此实验检验光子是否具有非零的静止质量一直备受关注.非零光子静止质量以Proca方程组为基础,其实验检验主要针对真空光速（频率）色散效应、库仑反平方定律和安培环路定律的偏离、寻找纵向电磁波以及磁偶极场的Yukawa势等几个方面.文章作者所在的实验小组采用精密扭秤调制方法将国际上同类实验结果提高了2个数量级,给出光子静止质量上限为mγ≤1.5×10-52g.对光子静止质量的实验检验,也是对光速不变原理的一种检验,即使光子仅有     

Cartan's contortion as a system of spin-2 and spin-0 fields

In several previous papers the author proposed to consider Cartan's contortion as a gauge field of Lorentz-group mediated by a massless spin-2 fields twin. In this article it is shown that these fields may be accompanied by a further pair of massive or massless spin-0 fields. Unfortunately, the study of the interaction of contortion with a Proca field shows that there is no reasonable macroscopic source generating the contortion. This defect is essential; the contortion mediated by standard fields can hardly exist in nature.     

Zitterbewegung of Bosons

Physics of Particles and Nuclei Letters - Zitterbewegung of massive and massless scalar bosons and a massive Proca (spin-1) boson is analyzed. The equations describing the evolution of the velocity...     

DERIVATION OF THE LEHNERT FIELD EQUATIONS FROM GAUGE THEORY IN VACUUM: SPACE CHARGE AND CURRENT

It is shown that the Lehnert field equations in vacuum, with concomitant space charge and current, can be derived straightforwardly from standard gauge theory applied in vacuum, using the concept of covariant derivative and Feynman's universal influence. The Lehnert and Proca field equations are shown to be inter-related through the well-known de Broglie theorem, in which the photon mass can be interpreted as finite. These ideas go some way towards addressing the inconsistency inherent in Maxwell's famous displacement current, which has no concomitant vacuum space charge.     

Operator Derivation of the Gauge-Invariant Proca and Lehnert Equations; Elimination of the Lorenz Condition

Using covariant derivatives and the operator definitions of quantum mechanics, gauge invariant Proca and Lehnert equations are derived and the Lorenz condition is eliminated in U(1) invariant electrodynamics. It is shown that the structure of the gauge invariant Lehnert equation is the same in an O(3) invariant theory of electrodynamics.     

Majorana-Oppenheimer Approach to Proca Field Equations

A Dirac-like equation for a massive field obeying the classical Proca equations of motion (PMO) is proposed in close analogy with Majorana’s construct for Maxwell electrodynamics. Its underlying algebraic structure is examined and a plausible physical interpretation is discussed. The behavior of the PMO equations in the presence of an external electromagnetic field is also investigated in the low energy limit, via unitary transformations similar to the Foldy-Wouthuysen canonical transformation for a Dirac fermion.     

Quantum wave equations and non-radiating electromagnetic sources

A connection between classical non-radiating sources and free-particle wave equations in quantum mechanics is rigorously made. It is proven that free-particle wave equations for all spins have currents which can be defined and which are non-radiating electromagnetic sources. It is also proven that and the advanced and retarded fields are exactly equal for these sources. Implications of these results are discussed.