Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics

Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that the Schrödinger equation admits an analogous treatment. We present a Lagrangian theory of a real scalar field φ whose equation of motion turns out to be equivalent to the Schrödinger equation with time independent potential. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics. The field φ is in the same relation to the real and imaginary part of a wave function as the vector potential is in respect to electric and magnetic fields. Preservation of quantum-mechanics probability is just an energy conservation law of the field φ.     

Relations between the electromagnetic form factors of the 0−- and 1−-mesons from the collinear groupsSU(3)⊗SU(3)⊗U(1) andSU(6) W

The relations between the electromagnetic matrix elements of the 18 low lying pseudoscalar and vector mesons predicted by the collinear groupsSU(3)?SU(3)?U(1) andSU(6) _W are derived. Using the hermiticity of the electromagnetic current operator, charge conjugation invariance and invariance under the full Lorentz group andSU(3)-symmetry separately, all electromagnetic matrix elements of these mesons are described by seven independent real form factors. After combining space-time with intrinsic properties of the particles this number is reduced to four by the minimal collinear groupSU(3) ?SU(3) ?U(1) and to three bySU(6) _W which involves more speculative assumptions. In the limit of low momentum transfer the predictions of both models become identical, depending on three real quantities. No disagreement with experiment has been found, as far as a comparison is possible.     

The Generalization of Chern-Simons Current and the Topological Tensor Current of <Emphasis Type="Italic">p</Emphasis>-Branes

To make the gauge field theory foundation of the topological current of p-branes introduced in our previous work, we present a novel topological tensor current in SO(N) gauge field theory. This non-Abelian gauge field tensor current is the straightforward generalization of the Chern-Simons topological current of strings. By making use of the SO(N) gauge potential decomposition theory and the φ-mapping topological current theory, it is proved that the p-brane is created at every isolated zero of the Clifford vector field \(\overrightarrow{\phi }(x)\) and the charges carried by p-branes are topologically quantized and labelled by the winding number of the φ-mapping.     

A modification of Einstein–Schrödinger theory that contains both general relativity and electrodynamics

We modify the Einstein–Schrödinger theory to include a cosmological constant Λ _z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ _z is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λ _b which multiplies the nonsymmetric fundamental tensor, such that the total Λ =  Λ _z +  Λ _b matches measurement. The resulting theory becomes exactly Einstein–Maxwell theory in the limit as |Λ _z | → ∞. For |Λ _z | ~ 1/(Planck length)² the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10^?16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein–Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein–Infeld–Hoffmann (EIH) equations of motion match the equations of motion for Einstein–Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein–Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner–Nordström solution except for additional terms which are ~10^?66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein–Maxwell theory.     

Zener Tunneling between the Landau Levels in a Two-Dimensional Electron System with One-Dimensional Periodic Modulation

Nonlinear magnetotransport in a two-dimensional electron gas in one-dimensional lateral lattices fabricated from a selectively doped GaAs/AlAs heterostructure is investigated. One-dimensional potential modulation is imposed on the two-dimensional electron gas by means of a set of metal strips formed on the planar surface of Hall bars. The dependences of the differential resistance r_xx on the magnetic field B < 0.5 T are studied at a temperature T = 1.6 K in lattices with a period of a ≈ 200nm. It is shown that periodic oscillations in r_xx(1/B) occur in such lattices under the action of a current-induced Hall field due to Zener tunneling between Landau levels. Interference is found between Zener oscillations and commensurability oscillations of r_xx in two-dimensional electron systems with one-dimensional periodic modulation. The experimental results are qualitatively explained by the role of Landau bands in nonlinear transport at large filling factors.     

Microwave photoresistance of a two-dimensional electron gas in a ballistic microbar

The effect of millimeter microwave radiation on the electron transport of two-dimensional (2D) ballistic microbars formed on the basis of individual GaAs quantum wells at a temperature of T = 4.2 K in magnetic fields B < 0.6 T has been investigated. Differences have been revealed in the magnetic field dependences of the microwave photoresistance of a 2D electron gas in Hall bars with a length L and a width W for the cases L, W > l _p and L, W < l _p , where l _p is the electron mean free path for momentum. The microwave photoresistance in macroscopic bars (L, W > l _p ) is a periodic alternating function of the inverse magnetic field; in microbars (L, W < l _p ), it is a periodic positive function of 1/B. The experimental results indicate that the mechanisms of the microwave photoresistance of a 2D electron gas are different for macroscopic and microscopic bars.     

Singlet $$\tilde V$$ correlator within the instanton vacuum model

The correlator of singlet axial-vector and vector currents in the external electromagnetic field is studied within the instanton liquid model of the QCD vacuum. In the chiral limit, we calculate the longitudinal w _L ⁽⁰⁾ and transversal w _T ⁽⁰⁾ , with respect to the axial-vector index, invariant amplitudes at an arbitrary spacelike momentum transfer q. It is demonstrated how the anomalous longitudinal part of the correlator is renormalized at low momenta due to the presence of the U _A (1) anomaly.     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Electron excitation of nucleon resonances: Structure functions and transition form factors

The electron excitation of nucleon resonances is discussed both from the theoretical and from the experimental point of view. This discussion is based on a phenomenological approach that employs the conservation of the electromagnetic and vector-meson hadronic currents and the requirements of limiting chiral invariance. For the electron excitation of J^π=1/2^±,3/2^±,5/2^±,... nucleon resonances, the structure functions are defined in terms of Sachs transition form factors. The resulting resonance structure functions for l+N → l+R processes are used in parametrizing smooth (background) structure functions for l+N → l+X inelastic scattering.     

Parametric resonance in neutrino oscillations in periodically varying electromagnetic fields

It is shown that a parametric resonance may arise in neutrino oscillations in varying electromagnetic fields. For two types of electromagnetic fields—an amplitude-modulated electromagnetic wave and a transverse magnetic field that is constant in time, but which has an amplitude periodically varying in space—the probabilities of the ν _i ? ν _j neutrino transitions are found, and it is shown that the probability amplitudes increase with time for a specific choice of the parameters of external electromagnetic fields.     

Schrödinger equation in multiply connected spaces and phase optics

The magnetic vector potential\(\vec A\) in a field free spaceR ₀ cannot be removed by gauge transformations in general, ifR ₀ is multiply connected.Aharonov andBohm ¹ have noticed recently that\(\vec A\) therefore should have more physical meaning than only to give the magnetic field by differentiation. They could show that\(\vec A\) inR ₀ may influence the phase ofSchrödinger'sψ-function in an observable manner. We want to point out here that this influence can be expressed in a simple, general form: “A closed magnetic field line operates uponψ like ae Φ/?-phase-shifter placed on any area bounded by the field line.” Surface like phase shifters are familiar in phase optics. There exists a narrow relationship between electron scattering at magnetic fields and some special problems of phase optics. An electron phase contrast microscope is discussed.     

Ionization potential of a metal cluster containing vacancies

A consistent procedure for determining the ionization potential of a large metal cluster of radius R _{N, v} , consisting of N atoms and N _v vacancies, is proposed. The perturbation theory in small parameters R _v /R _{N, v} and L _v /R _v (Rv and L _v are average distance between vacancies and the length of electron scattering on vacancies, respectively) is constructed in the effective-medium approximation for the electron ground state energy. The effective vacancy potential profile, the electron scattering phase and length are calculated by the Kohn–Sham method for a macroscopic metal in the stable jelly model. The obtained analytical dependences can be useful to analyze the results of photoionization experiments and to determine the size dependence of the vacancy concentration, including that near the melting temperature.     

Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [?y(1 + β), x(1 ? β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| < 1 and hyperbolas for |β| > 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.     

Electromagnetic transition form factors of Λ → <Emphasis Type="Italic">ne</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> weak dilepton decay

Weak radiative decay Λ → ne⁺e^? depends in general on four independent electromagnetic transition form factors. These form factors can be fixed in an extended model of dominance of vector mesons, where the asymptotic behavior of form factors is in agreement with quark counting rules. The dependence of the branching ratio of the Λ → ne⁺e^? decay on the relative weight of four electromagnetic form factors is investigated.     

Magnetoresistance of a highly correlated electron liquid

The behavior in a magnetic field of a highly correlated electron liquid approaching the fermion condensation quantum phase transition from the disordered phase is considered. We show that, at sufficiently high temperatures T≥T*(x), the effective mass starts to depend on T, M* ∝T^?1/2. This T^?1/2 dependence of the effective mass at elevated temperatures leads to the non-Fermi liquid behavior of the resistivity, σ(T) ∝ T and at higher temperatures σ(T) ∝ T^3/2. The application of a magnetic field B restores the common T² behavior of the resistivity. The effective mass depends on the magnetic field, M*(B) ∝ B^?2/3, being approximately independent of the temperature at T≤T*(B) ∝ B^4/3. At T≥T*(B), the T^?1/2 dependence of the effective mass is reestablished. We demonstrate that this B-T phase diagram has a strong impact on the magnetoresistance (MR) of the highly correlated electron liquid. The MR as a function of the temperature exhibits a transition from negative values of MR at T→0 to positive values at T ∝ B^4/3. Thus, at T≥T*(B), MR as a function of the temperature possesses a node at T ∝ B^4/3.     

Zero differential resistance of a two-dimensional electron gas in a one-dimensional periodic potential at high filling factors

The nonlinear magnetotransport of a two-dimensional (2D) electron gas in one-dimensional lateral superlattices based on a selectively doped GaAs/AlAs heterostructure is studied. The one-dimensional potential modulation of the 2D electron gas is performed by means of a series of metallic strips formed on the surface of a heterostructure with the use of electron beam lithography and a lift-off process. The dependence of the differential resistance r_xx on the magnetic field B < 1.5T in superlattices with the period a = 400 nm at a temperature of T = 4.2 K is investigated. It is found that electronic states with r_xx ≈ 0 appear in one-dimensional lateral superlattices in crossed electric and magnetic fields. It is shown that states with r_xx ≈ 0 in 2D electronic systems with one-dimensional periodic modulation arise at the minima of commensurability oscillations of the magnetoresistance.     

Electroweak tests with τ leptons at LEP

We report on two sensitive tests of lepton universality carried out by the 4 LEP experiments at the Z⁰ pole. From measurements of the τ polarization in e⁺ e^?→τ ⁺ τ ^?, the ratios of the vector and axial vector coupling constants of the electron and the tau lepton to the weak neutral current are obtained to beg _{v e} /g _{a e} =0.066±0.015 andg _{V τ} /g _{A τ} =0.070±0.009 respectively. From measurement of the τ lifetime and the τ leptonic branching ratios, the ratio of the coupling constants describing weak leptonic decays of the τ and the μ is measured to beG _τ /G _μ =0.996±0.008.     

Electron spin precession in the field of an electromagnetic wave

The solution of the Dirac equation for an electron in the field of a plane circularly polarized electromagnetic wave having an arbitrary intensity and a phase velocity v _ph different from the speed of light c is obtained. This solution is shown to describe the previously unknown effect of electron spin precession that exceeds the known precession effects caused by radiative corrections by six and more orders of magnitude and opens new possibilities for control of the polarization of electrons and for realization of various resonance methods associated with the spin precession. The predicted effect is in agreement with symmetry principles; however, it disappears at v _ph=c and is not described by the known Volkov solution.     

The Effect of Specular Reflectances on the Interaction of an Electromagnetic <Emphasis Type="Italic">E</Emphasis> Wave with a Thin Metal Film Placed between Two Dielectric Media

The interaction of an electromagnetic E wave with a thin metal film placed between two dielectric media is calculated in the case of different specular reflectances q₁ and q₂ for the reflection of electrons from the surface of the thin metal layer, in the case of variations in the values of dielectric permittivities ε₁ and ε₂ of the media, and in the case of different values of angle of incidence θ of the electromagnetic wave. The behavior of reflection coefficient R, transmission coefficient T, and absorption coefficient A in relation to the frequency of the external field is analyzed.     

Excitation of the Classical Electromagnetic Field in a Cavity Containing a Thin Slab with a Time-Dependent Conductivity

We derive an exact infinite set of coupled ordinary differential equations describing the evolution of the modes of the classical electromagnetic field inside an ideal cavity containing a thin slab with the time-dependent conductivity σ(t) and dielectric permittivity ε(t) for the dispersion-less media. We analyze this problem in connection with the attempts to simulate the so-called dynamical Casimir effect in three-dimensional electromagnetic cavities containing a thin semiconductor slab periodically illuminated by strong laser pulses. Therefore, we assume that functions σ(t) and δε(t) = ε(t) ? ε(0) are different from zero during short time intervals (pulses) only. Our main goal here is to find the conditions under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). We obtain approximate solutions to the dynamical equations in the cases of “small” and “big” maximal values of the functions σ(t) and δε(t). We show that the single-mode approximation used in the previous studies can be justified in the case of “small” perturbations, but the initially excited field mode cannot be amplified in this case if the laser pulses generate free carriers inside the slab. The amplification could be possible, in principle, for extremely high maximum values of conductivity and the concentration of free carries (the model of an “almost ideal conductor”) created inside the slab under the crucial condition providing the negativity of the function δε(t). This result follows from a simple approximate analytical solution confirmed by exact numerical calculations. However, the evaluation shows that the necessary energy of laser pulses must be, probably, unrealistically high.