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The response of ion plasmas to external radiation fields is investigated in a quantum mechanical formalism.We focus on the total electric field within the plasma. For general bandpass signals three frequency regions can be distinguished in terms of the plasma frequency. For low frequencies, the external field is shielded. For high frequencies, the field is not modified. Resonant behavior of the plasma appears for frequencies near the plasma frequency: large internal electric fields and induced currents are present. These effects may be relevant for biological systems. The model is therefore extended to a two-species plasma and additional interactions are studied. The response is not essentially altered. To make the models more realistic, a so-called bath is included. In the weak coupling approximation the resonance frequency is shifted and some damping occurs. Finite temperature effects on the electric field are absent. The energy of the system, however, depends on temperature.

A selection of the literature on the statistical description of electromagnetic fields and complex cavities is concisely reviewed. Some essential concepts, for example, the application of the central limit theorem and the maximum entropy principle, are scrutinized. Implicit assumptions, biased choices of variables and constraints, and some mathematical flaws are identified and possibly corrected. The commonly accepted probability distribution for the electromagnetic field has, therefore, to be considered as a hypothesis, which has not been contradicted by experiments. The alternative promising random coupling model is discussed as well. Ideas on future research are presented.

The reception of electromagnetic signals depends on the polarisation matching of the transmitting and receiving antenna. The practical matching differs from the theoretical one because of the noise deterioration of the transmitted and eventually received electromagnetic field. In other applications, the polarisation parameters of the receiving antenna are not known. Both problems are addressed by means of statistical methods, analytical as well as simulation results are obtained. The variation of the noisy matching factor depends mainly on the signal-to-noise ratio. The resulting probability distribution for the polarisation matching factor in case of a stochastic receiver is independent of the phase difference, but strongly affected by the axis ratio of the incident polarised field.

We examine commonly used approaches to deal with the scattering of electrons from a bound nucleon. Several prescriptions are shown to be related by gauge transformations. Nevertheless, due to current nonconservation, they yield different results. These differences reflect the size of the uncertainty that persists in the interpretation of ({ital e},{ital e}{sup {prime}}{ital p}) experiments. {copyright} {ital 1996 The American Physical Society.}

The multipole expansion of a general plane polarised electromagnetic field is derived. This is accomplished by calculating the coefficients of the dynamical multipole expansion of electromagnetic fields, representing generic solutions of the Maxwell equations in a source-free region. The analytical results are confirmed by comparing the suitably terminated expansions to the exact fields.

To evaluate a system or platform on its electromagnetic compatibility generally involves the application of several EMC standards. In order to compare applicable standards, one needs a common denominator as a basis. In this study, EMC norms for electromagnetic radiation are assessed statistically. A framework describing stochastic electromagnetic fields is applied and at the hand of the examples of military (MIL) and international electrotechnical commission (IEC) standards further developed for this purpose. The formalism not only evaluates such requirements but also enables the comparison of different standards in a probabilistic way. First illustrative results are presented. Frequency bands are identified for which IEC complying equipment exceeds the MIL standard with high probability.

Within the canonical Weyl gauge formulation, the axial gauge representation of QCD on a torus is derived. The resolution of the Gauss law constraint is achieved by applying unitary gauge fixing transformations. The result of this formal development is a Hamiltonian explicitly formulated in terms of unconstrained degrees of freedom. Novel features of this Hamiltonian are the non-perturbative dynamics of two-dimensional degrees of freedom appearing in the gauge-fixing procedure, such as Jacobian and centrifugal barrier. These two-dimensional fields appear to be essential for the infrared properties of the theory. The global residual gauge symmetries of QCD are established in this representation. It is shown that SU(N) gauge theories may exhibit at most N-1 massless vector (gauge) bosons. The implications for the phase structure of non-abelian gauge theories (QCD, Georgi-Glashow model) are discussed.

In the framework of the canonical Weyl gauge formulation of QED, the quantum mechanics of gauge fixing is discussed. Redundant quantum mechanical variables are eliminated by means of unitary transformations and Gauss′s law. This results in representations of the Weyl-gauge Hamiltonian which contain only unconstrained variables. As a remnant of the original local gauge invariance global residual symmetries may persist. In order to identify these and to handle infrared problems and related "Gribov ambiguities," it is essential to compactify the configuration space. Coulomb, axial, and light-cone representation of QED are derived. The naive light-cone approach is put into perspective. Finally, the Abelian Higgs model is studied; the unitary gauge representation of this model is derived and implications concerning the symmetry of the Higgs phase are discussed.

The global residual gauge symmetry of electrodynamics, the displacement symmetry, is discussed within the Weyl-gauge formulation and used to characterize different phases of the Maxwell field coupled to matter. Unlike other global symmetries, the displacement symmetry, in the absence of interactions or in the weak coupling regime, is realized in the Nambu-Goldstone mode. The displacement symmetry will be shown to be realized in the Wigner-Weyl mode in the plasma and superconducting states; this discussion develops a novel perspective of the plasma oscillations. Other examples are the states of the Schwinger model and the non-perturbative phase of the Abelian Higgs model. The Higgs mechanism is interpreted as formation of a phase with a high degree of symmetry. Finite photon mass and shielding of external fields will be recognized as the characteristic properties of these symmetric phases.

In a Lagrange formulation of nonrelativistic quantum mechanics gauge invariance corresponds to a local U(1) symmetry of the Lagrangian density. We review how this gauge symmetry yields the electromagnetic interaction of the free and the locally interacting N-body system and why nonlocal interactions require additional exchange contributions. A nonrelativistic Ward-Takahashi identity is then derived. This relates electromagnetic operators to the full propagator of the particles in question, which may be off their energy shell.

We comment on electron scattering from a bound nucleon. The general structure of the electromagnetic vertex of an off-shell nucleon, and constraints due to symmetries and gauge invariance are examined. The approximations necessary to arrive at commonly used recipes for the off-shell interaction are discussed. We put them into perspective by giving order of magnitude estimates for these approximations.

Detection and localisation of hidden magnetic objects is studied. The concomitant disturbance of the earth magnetic field is exploited. Magnetic fields and or gradients are measured with a number of sensors. Two point models for magnetic fields are selected for the analysis: the magnetic dipole and its quadrupole extension. It is shown how to apply least squares analysis of the data in order to detect and localise magnetised objects. The theoretical framework is tested in simulations, including noise. Two methods to do the minimisation are chosen. The formalism performs well in the simulations. Detection and localisation of the model objects is successful. No decisive differences in performance of the two minimisation methods are found. Results for the position parameters are reliable in any case. We have evaluated the goodness of fit in our simulations. Theoretical and simulated chi-square distributions are compared for different fit models and noise distributions with satisfactory results. The obtained parameter distributions are Gaussian. Measurements are performed to test the algorithms on real data collected for three ferromagnetic objects: a magnet, pipe and block. The magnet is easily localised, the pipe reasonably well. The block cannot be localised: its field variations cannot be distinguished from background field variations. Subsequent simulations show that using gradiometers improves the performances of the algorithms. The effects of a number of controllable parameters are evaluated. © The Institution of Engineering and Technology 2007.

The Jiles-Atherton model of the behavior of ferromagnetic materials determines the irreversible magnetization from the effective field by using a differential equation. This paper presents an exact, analytical solution to the equation, one displaying hysteresis. The inclusion of magnetomechanical couplings for various forms of the magnetostriction does not modify this solution. Consequently, the approach followed here is also very useful to study the effects of stress on the hysteretic magnetization.

The low-energy theorem (LET) prediction for neutral pion photoproduction on the proton remains valid even if isospin symmetry is broken. All rescattering effects are implicitly taken into account. Therefore, the data should not be corrected for final-state interactions in order to compare with the LET. As a consequence of such a correction, the previously quoted discrepancy between the LET and the experiment is overestimated.

We consider the effect of strong-vertex form factors on the gauge invariance of Born diagrams for the pion photoproduction reaction. The minimal-substitution prescription of Ohta for the electromagnetic current operator in pion photoproduction yields the same result as the simplest Born approach for one particular invariant amplitude. This is incompatible with recipes that multiply the Born amplitude by an overall form factor.

If a Goldstone symmetry is also explicitly broken, amplitudes are expected to be nonanalytical functions of the symmetry-breaking parameter and, consequently, of the induced mass of the Goldstone bosons. It is argued that the low-energy theorem for pion photoproduction on a nucleon, which yields the leading terms of the amplitude expanded in the physical pion-nucleon mass ratio, is not affected by this mechanism.

We consider a nonlocal quantum field theory, which can be used for the description of a composite particle, such as the nucleon interacting with its virtual pion field. Assuming a global symmetry of the theory, we discuss how to find the corresponding conserved currents. For the case of a U(1) symmetry, we then examine the conditions for second quantization and derive a general Ward-Takahashi identity. The formalism is then applied to the electromagnetic interaction.

The derivation of the low energy theorem for threshold photoproduction of neutral pions on a nucleon is reconsidered. Instead of considering explicitly the Born terms, as done in earlier derivations, a more general class of diagrams is separated from the total amplitude. Gauge invariance is imposed on the operator level and the partial conservation of the axial-vector current constraint is incorporated. Besides recovering the older results in this approach, relations for the off-shell behavior of the strong and electromagnetic vertices are derived.

Exploiting several arrays of sensors enables simultaneous detection of a number of emitters. Fusion of the respective array data yields lines containing possible positions as a function of the frequency. Identifying multiple intersections eventually leads to unambiguous localisation of the sources. The usual unwanted ghost detections do not appear in this approach. Simulations are performed to demonstrate the feasibility of the formalism.

We comment on the description of electromagnetic reactions involving hadrons, when the internal structure of the hadrons is taken into account. General off-shell vertex operators, only constrained by Lorentz and gauge invariance, are used. The electromagnetic production of pions on a nucleon is discussed as an example. Commonly used ad hoc recipes involving phenomenological form factors are discussed in the framework of an exact formulation.