E. Kazes

Nonrelativistic quantum mechanics and the anomalous part of the electron g factor

The departure of the electron g factor from 2 is calculated using a nonrelativistic theory of the electron interacting with the quantized transverse electromagnetic field. Although the magnetic moment correction δμ, due to the radiation field, is antiparallel to the magnetic moment μ0 of the bare electron, it is shown that the g factor correction is positive for a reasonable cutoff. This is due to the fact that the g factor is defined as the magnetic moment in units of the ’’physical’’ Bohr magneton. The role of mass renormalization is emphasized in this approach, and it is shown that the experimental g factor emerges for a cutoff of 0.53 electron masses.

Gauge Invariance and Gauge Independence of the S Matrix in Nonrelativistic Quantum Mechanics and Relativistic Quantum Field Theories

Abstract The gauge independence of transition rates as opposed to the gauge invariance of the equations of motion and gauge dependence of operators and state vectors is critically examined and explicitly demonstrated, both in nonrelativistic quantum mechanics and quantum field theory. Time independent as well as time dependent gauge transformations are explicitly analyzed using several techniques in order to clarify the physical content and significance of gauge independence and the conditions for its applicability.

Solution of an Integral Equation in V — θ Scattering

The Muskhelishvili method is used to obtain the off‐the‐mass‐ shell V — θ scattering amplitude.

Computer simulation of a wave packet tunneling through a square barrier

It is shown that, for energies E<or=V/sub 0/, the barrier height, the typical tunneling time is on the order of 10/sup -15/ s. The traversal time as a function of kinetic energy is locally symmetric near E=V/sub 0/. The tunneling time depends on the shape of the wave packet. The tunneling time is linearly dependent on barrier thickness for a wave packet with finite width. These conclusions are compared with the results obtained from other methods for estimating tunneling times.

Reply to comment on “variational formulation for the equilibrium condition of a conducting fluid in an electric field”

In this comment we respond to the several criticisms of the paper by Sujatha et al. raised by Kingham and Bell. In particular, we demonstrate that, contrary to their assertion, Taylors solution for the electrostatic fields can never satisfy the boundary conditions for the actual experimental configurations involving field emission liquid metal ion sources and other experiments on electrostatically stressed conducting fluids. It is further argued that a careful analysis of Taylors experimental procedure and observations suggests that although the observed static structures have a macroscopic axial-symmetry they have not the idealized conical shapes of prescribed angle. Furthermore, the formation of the Taylor cone structure is shown to be inconsistent with the principle of energy minimization.It is concluded that none of the criticism raised by Kingham and Bell invalidate any of the analysis or conclusions presented in the paper by Sujatha et al.

The physical significance of gauge independence and gauge covariance in quantum mechanics

The distinction between gauge independence and gauge covariance in electrodynamics is considered for quantities of physical interest. The gauge independence of directly observable quantities, such as the spectra of operators and energy conserving transition rates, is discussed and contrasted with the gauge covariance of other quantities such as scalar products. The quasigauge-invariance of the classical Lagrangian and the invariance of the Euler-Lagrange equations under the addition of a total time derivative to the Lagrangian are discussed. The consequent inherent nonuniqueness of the Lagrangian and Hamiltonian formulations of classical mechanics is pointed out. A physical interpretation of the explicit gauge dependence of classical canonical momenta and of the expectation values of the corresponding quantum mechanical operators is presented. The gauge independence of energy conserving transition rates calculated in the conventional finite-order time dependent perturbation theory is discussed and illustrated. The gauge dependence of the conventional time dependent transition amplitudes in the presence of electromagnetic fields is then discussed, and gauge independent transition amplitudes are constructed. An alternative formulation of the quantum mechanics of charged particles is obtained in terms of a new gauge independent Hamiltonian, which is, as might be expected, unique only within an arbitrary canonical transformation.

On the construction of gauge independent transition amplitudes

Abstract The conventional time dependent transition amplitude between a state ψ A ( t ), in the presence of an external electromagnetic field described by the four-potential A μ , and an eigenfunction of the field-free hamiltonian H 0 has been shown to depend on the gauge used to describe the fields. This is a serious flaw, and may underlie the continuing difficulties with the interpretation of Lamb shift measurements recently discussed by Low and Lundeen et al. Aharonov and Au have demonstrated the connection between gauge changes and the corresponding changes in the representation of the field-free hamiltonian. We complete the explicit proof of the existence of gauge independent transition amplitudes by an explicit construction of the field-free hamiltonian as a functional of the four potential used to describe the fields. This construction clarifies the procedure suggested by Aharonov and Au, assures the gauge independence of the transition amplitudes, and avoids the introduction of a preferred gauge advocated by Yang and collaborators.

An inverse mass approximation to the saturation of the algebra of vector densities

SummaryA new approximation to the saturation of the algebra of vector densities with low-lying states is proposed in which the neglected contributions are proportional to the inverse masses of the resonances concerned. The technique is applied with surprising success to the nucleon electromagnetic form factors in the lowest possible approximation.RiassuntoSi propone una nuova approssimazione alla saturazione dell’algebra delle densità vettoriali con stati inferiori, in cui i contributi trascurati sono proporzionali all’inverso delle masse delle risonanze interessate. Si applica questa tecnica con sorprendente successo ai fattori di forma elettromagnetici dei nucleoni nella approssimazione più bassa possibile.РезюмеПредлагается новое приближение для насыщения алгебры векторных плотностей с низко-лежащими состояниями, в котором пренебрегается вкладами, пропорциональными обратным массам рассматриваемых резонансов. Эта техника применяется, с поразительным услехом, для нуклонных электромагнитных форм-факторов в наинизщем возможном приближении.

Theoretical study of the field distributions in a linear electrohydrodynamic charged particle source for space applications

Abstract Electrohydrodynamic sources have been proposed as thrusters in electric space propulsion. Compared with chemical propulsion, electric propulsion is characterized by a relatively low thrust and high exhaust velocity of the propellant. These inherent characteristics of electric propulsion offer direct applications in space missions. A study of a field emission electric propulsion system has centered around an emitter modular unit. This module has evolved from a simple single-pin or point source emitter, through linear arrays of stacked needles to the solid slit type emitter module used by Bartoli et al. [J. Phys. D: Appl. Phys. L7 (1984) 2473; J. IEEE Trans. Plasma Sci. P515 (1987) 593]. To model the device, Mitterauer assumed the liquid metal emitter to be an infinitely long cylinder. In order to preserve the symmetry and make the problem tractable, he assumed the accelerator electrode to be a concentric cylinder, which was then used to study the condition for the onset of instability within a surface capillary wave model. Although this model can be used to estimate the field, it does not exhibit the actual geometry associated with the finite size in the device. In this paper, we use a more accurate model to simulate the experimental configuration. The electric field distributions for a finite slit-type liquid metal charged particle source emitter with a parallel planar anode are calculated using an analytic truncated series solution of Laplaces equation. This approach obviates the difficulties of the finite element method which becomes computationally less efficient when there are large gradients in the electric field. The form of the charge density on the emitter is approximated by a truncated series whose coefficients are determined by the boundary conditions on the emitter and the anode. The electric potential and field distribution are determined in both the plane perpendicular to the slit and in the plane of the slit. The calculated field distribution, as a function of scale of the device, suggests the significance of geometry for controlling the spatial characteristics of the emitted current density.

Generalized gauge independence and the physical limitations on the von Neumann measurement postulate

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the canonical momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a “mechanical” (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields.