Transformation Of Electromagnetic Field Research Articles

Gauge-invariant canonical quantisation of the electromagnetic field and duality transformations

The free electromagnetic field is canonically quantised in a gauge-invariant way by interpreting the Fourier coefficients of the magnetic induction field B as generalised coordinates, and the coefficients of the electric field E as their conjugate momenta. The usual commutation relations among the components of E and B are obtained. A canonical transformation, corresponding to a rotation in generalised phase space, is made on the Fourier coefficients. This transformation is shown to give a duality transformation on the electric and magnetic fields. The free-field Maxwell equations and the commutation relations are invariant under duality transformations. However, if interactions are introduced, the invariance under duality transformations is broken, and the original canonical theory should be used.

Electromagnetic field transformation upon change in properties of the medium with time within a limited region

Various applications often require knowledge of the signal exiting from a region whose properties vary with time. In the present study a simple model (sharp change in medium properties, i.e., ionization, in a semispace) will be used to consider the special features of field transformation upon change in medium parameters within a limited region, and also the field of the electromagnetic wave exiting this region. A solution for the nonstationary problem is constructed. Transformation of harmonic waves in an unbounded medium as the properties of the latter change has been considered several times [I-3]. Examples of pulse solutions in a dispersive medium with no boundaries were considered in [4, 5]. I. Let a planar electromagnetic wave propagate in the positive x direction of a Cartesian coordinate system within a medium whose dielectric and magnetic properties we will neglect. At time t = 0 at x O n=noh(--x) h(t), fz(s)= O, s<O' where h(s) is the Heaviside function. We assume that the ions are immobile and that the directional velocity of the electrons at the moment of formation is equal to zero, and we neglect collisions. Since the solution will depend on a single spatial coordinate x and the time t, T = ct (where c is the velocity of light in vacuo), the basic equations will have the form. c)Ey _ OB~ aB~ ~Ey 4~ a vy e Ox O"c Ox & + -- envy,

G−2Experiments as a Test of Special Relativity

An analysis of $g\ensuremath{-}2$ and lifetime measurements for electrons and muons at various velocities is used to compare the transformation of time, electromagnetic field, and mass in moving coordinate systems and to check the Thomas precession. The data are in good agreement with the special theory of relativity.

Relativistic transformation of the Newtonian force and the electromagnetic field transformations

Relativistic transformation of the Newtonian force and the electromagnetic field transformations

Chiral (γ5) symmetry of massless fields and neutrino theory of photons

It is shown that the field theory of massless particles has the internal symmetry groupG=U(1) ⊗ AutU(1). The γ5 and dual transformations of neutrino and electromagnetic fields are particular cases of the transformations of this group. TheCP transformations of massless field can also be included in the transformations of this group. The following formulation of Pryce (1938) theorem is given: Statistical properties of the composite photon in the neutrino theory of light are inconsistent with chiral (γ5) symmetry of neutrino and electromagnetic fields.

Transformation of the Spectrum of a Signal in Communication between Relativistically Moving Inertial Frames

Future space exploration may involve communications between spacecraft moving at relativistic velocities. One of the significant problems associated with such communication is spectral distortion of signals which are propagated between relativistic frames. This distortion is generated by both changing propagation distances and purely relativistic electromagnetic field transformations. In this paper a linear integral transformation is formulated for relating the Fourier spectra of the source antenna excitation current and the resulting incident electric field at the receiving antenna. The kernel of the transformation is evaluated for the case of a steerable source antenna tracking on the advanced receiver position. The transformation is then applied to the case of an ideal thin-wire half-wave dipole source antenna excited by a narrowband, double-sideband modulated current. The specific distortions of spectral spreading and translation are then related to increased bandwidth and upper cutoff frequency requirements of receiving systems in relativistic applications.

Transformation of Small-Signal Energy and Momentum of Waves

The transformation of the small-signal energy and momentum of a wave between two inertial reference frames as first given by Sturrock are derived by using simple perturbation theory and the appropriate transformations of length, time, current, and electromagnetic fields. The approach allows a straightforward generalization to the case of relativistic linear transformations and to nonrelativistic transformations between two reference frames that rotate with respect to each other. These rotating and linear transformations allow one to make very general statements about the frequency and wavenumbers for which negative-energy waves are obtained in a rotating and translating medium, as, for example, an electron beam in Brillouin flow.