Electromagnetic Field Strength Tensor Research Articles

Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction

Abstract The Weyl double copy builds the relation between gauge theory and gravity theory, especially the correspondence between gauge solutions and gravity solutions. In this paper, we obtain the slowly rotating charge solutions from the Weyl double copy for the Kerr black hole with small Chern-Simons correction. Based on the Weyl double copy relation, for the Petrov type D solution in Chern-Simons modified gravity, we find the additional correction to the electromagnetic field strength tensor of the rotating charge. For the Petrov type I solution, we find that the additional electromagnetic field strength tensors have external sources, while the total sources vanish at the leading order.

Classification of generalised higher-order Einstein-Maxwell Lagrangians

We classify all higher-order generalised Einstein-Maxwell Lagrangians that include terms linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength tensor. Using redundancies due to the Bianchi identities, dimensionally dependent identities and boundary terms, we show that a general Lagrangian of this form can always be reduced to a linear combination of only 21 terms, with coefficients that are arbitrary functions of the two scalar invariants derived from the field strength. We give an explicit choice of basis where these 21 terms include 3 terms linear in the Riemann tensor and 18 terms quadratic in the derivatives of the field strength.

Dark matter effective field theory and an application to vector dark matter

The Standard Model Effective Field Theory (SMEFT) and the Low Energy Effective Field Theory (LEFT) can be extended by adding additional spin 0, 1/2 and 1 dark matter particles which are singlets under the Standard Model (SM) gauge group. We classify all gauge invariant interactions in the Lagrangian up to terms of dimension six, and present the tree-level matching conditions between the two theories at the electroweak scale. The most widely studied dark matter models, such as those based on the Higgs portal or on kinetic mixing between the photon and a dark photon, are based on dimension-four interactions with the SM sector. We consider a model with dark vector particles with a ℤ2 symmetry, so that the lightest dark matter particle is stable. The leading interaction with the SM is through dimension-six operators involving two dark vector field-strength tensors and the electromagnetic field-strength tensor. This model is a viable dark matter model in the freeze-in scenario for a wide range of parameters.

Second gradient electrodynamics: A non-singular relativistic field theory

In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the energy–momentum tensor and the Lorentz force density are presented. For a point charge, the generalized Liénard–Wiechert potentials and the corresponding electromagnetic field strength tensor are given as retarded integral expressions. Explicit formulas for the electromagnetic potential vector and electromagnetic field strength tensor of a uniformly moving point charge are found without any singularity and discontinuity. In addition, a world-line integral expression for the self-force of a charged point particle is given. The relativistic equation of motion of a charged particle coupled with electromagnetic fields in second gradient electrodynamics is derived, which is an integro-differential equation with nonlocality in time. For a uniformly accelerated charge, explicit formulas of the self-force and the electromagnetic mass, being non-singular, are given. Moreover, the wave propagation and the dispersion relations in the vacuum of second gradient electrodynamics are analyzed. Three modes of waves were found: one non-dispersive wave as in Maxwell electrodynamics, and two dispersive waves similar to the wave propagation in a collisionless plasma.

Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors

A compatible spin 1 spinor representation with Clifford algebra (1,3) (or 1,3 Cl ) is derived for both (1 / 2,1 / 2) and (1, 0) (0,1)  Lorentz group representations with spin 1/2 particles Dirac spinors in 1,3 Cl . The relation between the two different representations of spin 1 spinors is analogous to the relation between the electromagnetic vector potential field A and the electromagnetic field strength tensor F  . From this relationship, the two representations are combined by the formula u( p, )  ( p, )  p / m. We also note that the Grassmann basis provides more convenient basis for spin 1 spinors especially in chiral representations of (1, 0) (0,1)  , even though the Clifford basis is more fitting for spin 1/2 and (1/ 2,1/ 2) spinor representations for both helicity and handedness.

Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

We construct the Rarita–Schwinger basis vectors, [Formula: see text], spanning the direct product space, [Formula: see text], of a massless four-vector, [Formula: see text], with massless Majorana spinors, [Formula: see text], together with the associated field-strength tensor, [Formula: see text]. The [Formula: see text] space is reducible and contains one massless subspace of a pure spin-[Formula: see text]. We show how to single out the latter in a unique way by acting on [Formula: see text] with an earlier derived momentum independent projector, [Formula: see text], properly constructed from one of the Casimir operators of the algebra [Formula: see text] of the homogeneous Lorentz group. In this way, it becomes possible to describe the irreducible massless [Formula: see text] carrier space by means of the antisymmetric tensor of second rank with Majorana spinor components, defined as [Formula: see text]. The conclusion is that the [Formula: see text] bi-vector spinor field can play the same role with respect to a [Formula: see text] gauge field as the bi-vector, [Formula: see text], associated with the electromagnetic field-strength tensor, [Formula: see text], plays for the Maxwell gauge field, [Formula: see text]. Correspondingly, we find the free electromagnetic field equation, [Formula: see text], is paralleled by the free massless Rarita–Schwinger field equation, [Formula: see text], supplemented by the additional condition, [Formula: see text], a constraint that invokes the Majorana sector.

Reissner–Nordstrom metric in unimodular theory of gravity

We study the modified Reissner–Nordstrom (RN) metric in the unimodular gravity. So far the spherical symmetric Einstein field equation in unimodular gravity has been studied in the absence of any source. We consider static electric and magnetic charge as source. We solve for Maxwell equations in unimodular gravitational background. We show that in unimodular gravity, the electromagnetic field strength tensor is modified. We also show that the solution in unimodular gravity differs from the usual RN metric in Einstein gravity with some corrections. We further study the thermodynamical properties of the RN black hole solution in this theory.

Gyromagnetic gs factors of the spin-1/2 particles in the (1/2+-1/2--3/2-) triad of the four-vector spinor, ψμ, irreducibility and linearity

The gauged Klein–Gordon equation, extended by a gsσμνFμν/4 interaction, the contraction of the electromagnetic field strength tensor, Fμν, with the generators, σμν/2, of the Lorentz group in (1/2, 0) ⊕ (0, 1/2), and gs being the gyromagnetic factor, is examined with the aim to find out as to what extent it qualifies as a wave equation for general relativistic spin-1/2 particles transforming as (1/2, 0) ⊕ (0, 1/2) and possibly distinct from the Dirac fermions. This equation can be viewed as the generalization of the gs = 2 case, known under the name of the Feynman–Gell-Mann equation, the only one which allows for a bilinearization into the gauged Dirac equation and its conjugate. At the same time, it is well-known a fact that a gs = 2 value can also be obtained upon the bilinearization of the nonrelativistic Schrödinger into nonrelativistic Pauli equations. The inevitable conclusion is that it must not be necessarily relativity which fixes the gyromagnetic factor of the electron to g(1/2) = 2, but rather the specific form of the primordial quadratic wave equation obeyed by it, that is amenable to a linearization. The fact is that space-time symmetries alone define solely the kinematic properties of the particles and neither fix the values of their interacting constants, nor do they necessarily prescribe linear Lagrangians. Information on such properties has to be obtained from additional physical inputs involving the dynamics. We here provide an example in support of the latter statement. Our case is that the spin-1/2- fermion residing within the four-vector spinor triad, ψμ ~ (1/2+-1/2--3/2-), whose sectors at the free particle level are interconnected by spin-up and spin-down ladder operators, does not allow for a description within a linear framework at the interacting level. Upon gauging, despite transforming according to the irreducible (1/2, 1) ⊕ (1, 1/2) building block of ψμ, and being described by 16-dimensional four-vector spinors, though of only four independent components each, its Compton scattering cross sections, both differential and total, result equivalent to those for a spin-1/2 particle described by the generalized Feynman–Gell-Mann equation from above (for which we provide an independent algebraic motivation) and with g(1/2-) = -2/3. In effect, the spin-1/2- particle residing within the four-vector spinor effectively behaves as a true relativistic "quadratic" fermion. The g(1/2-) = -2/3 value ensures in addition the desired unitarity in the ultraviolet. In contrast, the spin-1/2+ particle, in transforming irreducibly in the (1/2, 0) ⊕ (0, 1/2) sector of ψμ, is shown to behave as a truly linear Dirac fermion. Within the framework employed, the three spin sectors of ψμ are described on equal footing by representation- and spin-specific wave equations and associated Lagrangians which are of second-order in the momenta.

Searching for CPT Violation with Cosmic Microwave Background Data from WMAP and BOOMERANG

We search for signatures of Lorentz and $CPT$ violations in the cosmic microwave background (CMB) temperature and polarization anisotropies by using the Wilkinson Microwave Anisotropy Probe (WMAP) and the 2003 flight of BOOMERANG (B03) data. We note that if the Lorentz and $CPT$ symmetries are broken by a Chern-Simons term in the effective Lagrangian, which couples the dual electromagnetic field strength tensor to an external four-vector, the polarization vectors of propagating CMB photons will get rotated. Using the WMAP data alone, one could put an interesting constraint on the size of such a term. Combined with the B03 data, we found that a nonzero rotation angle of the photons is mildly favored: $\ensuremath{\Delta}\ensuremath{\alpha}=\ensuremath{-}6.0\genfrac{}{}{0}{}{+4.0}{\ensuremath{-}4.0}\genfrac{}{}{0}{}{+3.9}{\ensuremath{-}3.7}\text{ }\text{ }\mathrm{deg}(1,2\ensuremath{\sigma})$.

Searching forCPTViolation with Cosmic Microwave Background Data from WMAP and BOOMERANG

We search for signatures of Lorentz and violations in the cosmic microwave background (CMB) temperature and polarization anisotropies by using the Wilkinson Microwave Anisotropy Probe (WMAP) and the 2003 flight of BOOMERANG (B03) data. We note that if the Lorentz and symmetries are broken by a Chern-Simons term in the effective Lagrangian, which couples the dual electromagnetic field strength tensor to an external four-vector, the polarization vectors of propagating CMB photons will get rotated. Using the WMAP data alone, one could put an interesting constraint on the size of such a term. Combined with the B03 data, we found that a nonzero rotation angle of the photons is mildly favored: [Formula: See Text].

Renormalization of the vector current in QED

It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false, (b) how to obtain the renormalization of the current to all orders of perturbation theory, and (c) how to correctly define an electron number operator. The current mixes with the four-divergence of the electromagnetic field-strength tensor. The true electron number operator is the integral of the time component of the electron number density, but only when the current differs from the $\overline{\mathrm{MS}}$-renormalized current by a definite finite renormalization. This happens in such a way that Gauss's law holds: the charge operator is the surface integral of the electric field at infinity. The theorem extends naturally to any gauge theory.

Real irreducible sesquilinear-quadratic tensor concomitants of complex bivectors

Irreducible tensor concomitants of an arbitrary complex antisymmetric second rank tensor, or bivector, in a Minkowski space-time are presented. These tensors are quadratic in the complex bivector and invariant under an overall multiplicative phase change of the bivector; in other words, they are sesquilinear-quadratic tensor concomitants of the complex bivector. The tensors are real and irreducible under the full real Lorentz group. Particular consideration is given to when the complex bivector is the electromagnetic field strength tensor (complex description is appropriate for radiation), and it is found that some of these irreducible tensors are novel electromagnetic observables not previously mentioned in the literature.

Calculating the photonic condensate in perturbative QED

We consider the vacuum expectation value 〈0|Fμv2|0〉, where Fμv is the electromagnetic field strength tensor, and use the point splitting technique to regularize the calculation. Then 〈0|Fμv2|0〉 turns out to vanish in one-loop approximation. In higher orders the vacuum expectation value appears to be divergent but calculable in term s of the β-function within the regularization scheme specified.

Quantum Field Theoretic Treatment of the Casimir Effect at T > 0. Real Time Formalism — Free Field Approximation

AbstractThe framework of real time quantum field theory at finite temperature is generalized to include boundary conditions for the electromagnetic field strength tensor. In the perturbation theory the usual Feynman rules remain, only the photon propagator is modified. As a first application the Casimir effect is studied in the free field approximation and the known results are rederived with the new method.

Helmholtz theorem for antisymmetric second-rank tensor fields and electromagnetism with magnetic monopoles

A generalized Helmholtz’s theorem is proved, which states that an antisymmetric second-rank tensor field in 3+1 dimensional space-time, which vanishes at spatial infinity, is determined by its divergence and the divergence of its dual. When the divergence of the antisymmetric electromagnetic field strength tensor is equal to the electric charge-current density and the divergence of the dual of the electromagnetic field strength tensor is equal to the magnetic charge-current density, the equations of electromagnetism are obtained. As a convenience, in the solution of the equations of electromagnetism two different four-vector potentials can be used, one of which couples to the electric charge-current density and the other to the magnetic charge-current density.