A model of nonlinear electrodynamics

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.     

Vacuum local and global electromagnetic self-energies for a point-like and an extended field source

We consider the electric and magnetic energy densities (or equivalently field fluctuations) in the space around a point-like field source in its ground state, after having subtracted the spatially uniform zero-point energy terms, and discuss the problem of their singular behavior at the source’s position. We show that the assumption of a point-like source leads, for a simple Hamiltonian model of the interaction of the source with the electromagnetic radiation field, to a divergence of the renormalized electric and magnetic energy density at the position of the source. We analyze in detail the mathematical structure of such a singularity in terms of a delta function and its derivatives. We also show that an appropriate consideration of these singular terms solves an apparent inconsistency between the total field energy and the space integral of its density. Thus the finite field energy stored in these singular terms gives an important contribution to the self-energy of the source. We then consider the case of an extended source, smeared out over a finite volume and described by an appropriate form factor. We show that in this case all divergences in local quantities such as the electric and the magnetic energy density, as well as any inconsistency between global and space-integrated local self-energies, disappear.     

String-Localized Quantum Fields and Modular Localization

We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincaré group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representations and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting.Dedicated to Hans-Jürgen Borchers on the occasion of his 80th birthday     

Nonlinear arcsin‐electrodynamics

A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field is present the phenomenon of vacuum birefringence takes place. The indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field are calculated. The electric field of a point‐like charge is not singular at the origin and the static electric energy is finite. We have calculated the static electric energy of point‐like particles for different parameters of the model. The canonical and symmetrical Belinfante energy‐momentum tensors and dilatation current are obtained. We demonstrate that the dilatation symmetry and dual symmetry are broken in the model suggested.

     

A new local and lorentz-covariant solution of the schwinger model

We present a local, manifestly Lorentz-covariant operator solution of the Schwinger model for arbitrary gauge. The main features of our solution are: (i) there is a unique normalizable translation-invariant state, (ii) the electric and chiral charge are not spontaneously broken, i.e. they generate implementable symmetry transformations, (iii) on the physical subspace the vacuum is degenerate in energy with an infinite number of states of nonzero chirality, (iv) the electromagnetic tensor is simply proportional to a massive pseudo-scalar field.     

Nonlinear Electrodynamics and NED-Inspired Chiral Solitons

A nonlinear electrodynamics Lagrangian is considered and the electric field associated to an electric point-like charge is derived. The corresponding expression for the total field energy which has finite value in our model, is obtained. The chiral form of the Lagrangian is also presented. Topological, finite-energy, spherically symmetric solutions of the chiral model are studied and some of their properties are discussed.     

Integrability in Yang-Mills theory on the light cone beyond leading order

The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal-helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that, while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the ajoint SU(N(c)) matter it survives the conformal symmetry breaking and persists in supersymmetric N=1, N=2, and N=4 Yang-Mills theories.     

Electric strings and light-like lumps in classical electrodynamics

Soliton-like solutions of classical spinor electrodynamics with the symmetry of a cylinder of finite or infinite length are described. The solutions have non-vanishing total charge and, contrary to ordinary strings, an azimuthal magnetic and a radial electric field. For finite length, these lumps move with the velocity of light in the direction of the symmetry axis and the total four momentum is light-like. The crucial mechanism is a subtle compensation which prevents the matterfield from recoupling to its own electromagnetic field.     

Fermionic dispersion relations at finite temperature and non-vanishing chemical potentials in the minimal standard model

We calculate the fermionic dispersion relations in the minimal standard model at finite temperature in presence of non-vanishing chemical potentials due to the CP-asymmetric fermionic background. The dispersion relations are calculated for a vacuum expectation value of the Higgs field equal to zero (unbroken electroweak symmetry). The calculation is performed in the real time formalism of the thermal field theory at one-loop order in a general ζ gauge. The fermionic self-energy is calculated at leading order in temperature and chemical potential and this fact permits us to obtain gauge-invariant analytical expressions for the dispersion relations.     

Bianchi type I cosmology in generalized Saez–Ballester theory via Noether gauge symmetry

In this paper, we investigate the generalized Saez–Ballester scalar–tensor theory of gravity via Noether gauge symmetry (NGS) in the background of Bianchi type I cosmological spacetime. We start with the Lagrangian of our model and calculate its gauge symmetries and corresponding invariant quantities. We obtain the potential function for the scalar field in the exponential form. For all the symmetries obtained, we determine the gauge functions corresponding to each gauge symmetry which include constant and dynamic gauge. We discuss cosmological implications of our model and show that it is compatible with the observational data.     

Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.     

Unified Theory of Fundamental Interactions

Based on local gauge invariance, four different kinds of fundamental interactions in nature are unified in a theory which has SU(3)C( )SU SU(2)L( )U(1)( )s Gravitational Gauge Group gauge symmetry. In this approach,gravitational field, like electromagnetic field, intermediate gauge field, and gluon field, is represented by gauge potential.Four kinds of fundamental interactions are formulated in the similar manner, and therefore can be unified in a direct or semi-direct product group. The model discussed in this paper is a renormalizable quantum model and can be regarded as an extension of the standard model to gravitational interactions, so it can be used to study quantum effects of gravitational interactions.     

Casimir Vacuum Energy and the Semiclassical Electron

In 1953 Casimir proposed a semiclassical model for the electron based on the concept that net inward radiation pressure from the electromagnetic vacuum fluctuation fields (as in the Casimir effect, generally) might play the role of Poincare stresses, compensating outward coulomb pressure to yield a stable configuration at small dimensions. Given that in scattering experiments the electron appears point-like, critical to the success of the proposed model is demonstration that the self-energy corresponding to the divergent coulomb field does not contribute to the electron mass. Here we develop a self-consistent, vacuum-fluctuation-based model that satisfies this requirement and thereby resolves the issue of what would otherwise appear to be an incompatibility between a point-like electron and finite mass.     

On planar fermions with quartic interaction at finite temperature and density

We study the breaking of parity symmetry in the 2+1 Gross-Neveu model at finite temperature with chemical potential μ, in the presence of an external magnetic field. We find that the requirement of gauge invariance, which is considered mandatory in the presence of gauge fields, breaks parity at any finite temperature and provides for dynamical mass generation, preventing symmetry restoration for any non-vanishing μ. The dynamical mass becomes negligibly small as temperature is raised. Received 4 April 2002 / Received in final form 12 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: cabra@venus.fisica.unlp.edu.ar     

Non-inertial electromagnetic effects in matter. Gyromagnetic effect

Non-inertial electromagnetic effects in matter, i.e. electromagnetic fields created by a non-inertial motion of material bodies, are discussed within the Drude–Lorentz (plasma) model of matter polarization. It is shown that an oscillatory motion of a point-like body, or wavelike motion in an extended body gives rise to electromagnetic fields with the same frequency as the frequency of the original motion, while shock-like movements of a point-like body generate electromagnetic fields with the characteristic (atomic scale) frequency of the bodies. The polarization of a rigid body induced by rotations is discussed in various circumstances. A uniform rotation produces a static electric field in a dielectric and a stationary current (and a static magnetic field) in a conductor. The latter corresponds to the gyromagnetic effect (while the former may be called the gyroelectric effect). Both fields are computed for a sphere and the gyromagnetic coefficient is derived. A non-uniform rotation induces emission of electromagnetic fields. The equations of motion for the polarization are linearized for slight non-uniformities of the angular velocity and solved both for a dielectric and a conducting sphere. The electromagnetic field emitted by a dielectric spherically shaped body in (a slightly) non-uniform rotation has the characteristic (atomic scale) frequency of the body (slightly shifted by the uniform part of the angular frequency). In the same conditions, a conducting sphere emits an electromagnetic field whose frequency is double the uniform part of the angular frequency.     

Aharonov-bohm effect as the basis of electromagnetic energy inherent in the vacuum

The Aharonov-Bohm effect shows that the vacuum is structured, and that there can exist a finite vector potentialA in the vacuum when the electric field strengthE and magnetic flux densityB are zero. It is shown on this basis that gauge theory produces energy inherent in the vacuum. The latter is considered as the internal space of the gauge theory, containing a field made up of components ofA, to which a local gauge transformation is applied to produce the electromagnetic field tensor, a vacuum charge/current density, and a topological charge g. Local gauge transformation is the result of special relativity and introduces spacetime curvature, which gives rise to an electromagnetic field whose source is a vacuum charge current density made up ofA and g. The field carries energy to a device which can in principle extract energy from the vacuum. The development is given forU(1) andO(3) invariant gauge theory applied to electrodynamics. Former Edward Davies Chemical Laboratories, University College of Wales, Aberystwyth SY32 1NE, Wales, United Kingdom.     

On the 1-Loop Renormalization of the Electroweak Standard Model and its Application to Leptonic Processes

A renormalization scheme for the electroweak standard model is presented in which the electric charge and the masses of the gauge bosons, Higgs particle and fermions are used as physical parameters. The photon is treated such that quantum electrodynamics is contained as a simple substructure. Field renormalization respecting the gauge symmetry gives finite propagators and vertex functions. The Ward identities between the Green functions of the unphysical sector allow a renormalization that maintains the simple pole structure of the propagators in the t'Hooft-Feynman gauge. We give a complete list of self energies and all renormalization constants also in the unphysical Higgs and ghost sector. Explicit results are given for the renormalized self energies, vertex functions and boxes that enter the evaluation of 1-loop radiative corrections to fermionic processes. We calculate the 1-loop radiative corrections to purely leptonic reactions like μ decay, vμ_μe scattering and μ pair production in e⁺e⁻annihilation. A test of the standard model is performed by comparing these low energy data with the results of the PP collider experiments for the W and Z boson masses.     

Stability and decay of the Dirac vacuum in external gauge fields

We consider various gauge fields coupled to the free Dirac equation according to symmetry principles. The gauge fields are treated as classical, unquantized fields. Sufficiently strong time-independent fields may give rise to spontaneous particle creation and to the decay of the symmetric Dirac vacuum into a new ground state with broken symmetry. The vacuum stability of the Dirac field is studied for the cases of external electromagnetic (U(1)), gravitational (Poincaré group including torsion) and Yang-Mills (SU(2)) potentials.     

Hot gauge theories in external electromagnetic fields

A general treatment of finite temperature and external electromagnetic field effects for gauge theories is presented. The results are illustrated explicitly for the SU(2) model of Georgi and Glashow for which we obtain the finite temperature one-loop effective action in the presence of an external magnetic field. We discuss briefly the possible use of the results obtained.