A Novel Interpretation of the Klein-Gordon Equation

The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrödinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an initial boundary condition, this paper considers the possibility that the solutions are determined by both an initial and a final boundary condition. By constructing an invariant joint probability distribution from the size of the solution space, it is shown that the usual measurement probabilities can nearly be recovered in the non-relativistic limit, provided that neither boundary constrains the energy to a precision near ?/t ₀ (where t ₀ is the time duration between the boundary conditions). Otherwise, deviations from standard quantum mechanics are predicted.     

The Lamb shift in non-relativistic quantum electrodynamics

A new viewpoint concerning the calculation of the Lamb shift for an atomic ground state is presented in the framework of non-relativistic quantum electrodynamics. It is shown that a generalization of the Craig-Power transformation, developed to investigate long-range intermolecular forces, produces a new form for the non-relativistic hamiltonian. This hamiltonian enables the Lamb shift energy to be obtained as the expectation value of an effective interaction energy alone with no contribution from the expectation value of the unperturbed parts. This is in contrast with the necessity to find the expectation values for all three contributions in both the minimal coupled and the multipolar coupled forms of the hamiltonian for non-relativistic quantum electrodynamics.     

Relativistic electron-phonon interaction

On the basis of a new relativistic one-particle equation it is possible to reformulate the problem of the relativistic electron-phonon interaction in terms of “oscillating rigid muffin-tins” such that it can be expressed as in the non-relativistic case. The improvement over the non-relativistic approximation is shown for lanthanum and tungsten.     

PCAC and the non-relativistic pion-nucleon vertex

The Foldy-Wouthuysen reduction technique is applied to the sigma model and pseudovector coupling pion-nucleon Lagrangians. In contrast to electrodynamics the requirement that the non-relativistic pion-nucleon Lagrangian have an approximate symmetry under the same global transformation as the relativistic theory does not uniquely fix the Foldy-Wouthuysen transformation. It is shown that the partially conserved axial-vector current relation is satisfied by the non-relativistic theory and the implications of this on the form of the effective pion-nucleon vertex are discussed.     

A generalization of Wigner's R-matrix method

A generalization of the Wigner's non-relativistic R-matrix theory of scattering by a central potential field is proposed. The idea is to use an R-matrix expansion basis generated by a Sturm-Liouville problem with an eigenparameter included both in a differential equation and in a boundary condition (in the standard theory an R-matrix basis is obtained by solving an eigenvalue problem with fixed boundary conditions). A partial fraction expansion of an R^(η)-matrix introduced is derived and shown to converge faster than a partial fraction expansion of Wigner's R-matrix used in the standard theory.     

Plane-wave approximation in theS-matrix and the construction of bound-state wave functions

Three inversion problem approaches — byGelfand-Levitan, Marchenko andPetrá? [5] —in both non-relativistic and relativistic (Klein-Gordon) variants are used in an approximation scheme selected to construct bound-state wave functions which are advantageous for purposes of model hadron physics. This family of wave functions is created exclusively by theS-matrix quantities and derived in the approximation which requires the Jost function to be equal to the unity throughout the continuous spectrum (the plane-wave approximation). As a consequence of the difference in boundary conditions of the mentioned approaches, the resulting approximate wave functions are not identical, but it is shown that there exists a parallelism as to the form among them. This parallelism is explained more extensively in the non-relativistic case, where the transformation properties of alternative sets of functions are treated. In the present paper it is demonstrated that in the relativistic variants of the above approaches the non-relativistic plane-wave-approximation form of the constructed wave functions for a given bound state is preserved.     

The Boundary Condition in the Classical Derivation of the BBR

The classical derivation of the black body radiation (BBR) spectrum by Boyer was based on an equilibrium mechanism such that in the absence of thermal radiation particles in a container can gain kinetic energy from the random electromagnetic zero point field (ZPF) radiation. Their loss of that energy was to be by means of their collisions with the walls of the container. Theoretically, energy dissipation through collisions with the walls might lead to a divergent kinetic energy value for the particles. This is because the box can be taken large enough to minimize the collisions probability, and that can lead to a particle’s indefinite growth in energy. Furthermore, a derivation of a general phenomenon such as the BBR should be possible without relying on the walls boundary of a box. Therefore, a new boundary condition is proposed here which is related to relativistic effects. It is shown that with the new boundary condition one may still recover the BBR spectrum. A discussion is presented that shows how the new boundary condition is indeed responsible for energy dissipations.     

Landau quantization in the spinning cosmic string spacetime

We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e., having a finite width and uniformly filled with both material and vacuum energies.     

Mass gain and loss of non-relativistic electrons in photon-electron interactions

It is shown that the electrons gain mass as their non-relativistic velocities increase. This process is realized by the absorption of photons in the colliding process. In an inverse manner, they loss their mass when they radiate photons. The related equations are derived by using the relativistic mass equation and independently by considering the non-relativistic energy relation. The Compton scattering and photon emission phenomena are revisited with the new theory.     

Revisiting Cardassian model and cosmic constraint

Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) in semi-infinite space-time. In the non-relativistic limit (x???x,t??t,???0), the boundary conformal algebra changes to boundary Galilean conformal algebra (BGCA). In this work, some aspects of AdS/BCFT in the non-relativistic limit were explored. We constrain correlation functions of Galilean conformal invariant fields with BGCA generators. For a situation with a boundary condition at surface x=0 ( $z=\overline{z}$ ), our result agrees with the non-relativistic limit of the BCFT two-point function. We also introduce the holographic dual of boundary Galilean conformal field theory.     

Multiple-Rotor-Cycle QPASS Pulse Sequences: Separation of Quadrupolar Spinning Sidebands with an Application to La NMR

The quadrupolar phase-adjusted spinning sidebands (QPASS) pulse sequence has been recently demonstrated as a useful method for obtaining quadrupolar parameters with magic-angle spinning NMR. The sequence separates spinning sidebands by order in a two-dimensional experiment. A sheared projection of the 2D spectrum effectively yields the infinite spinning rate second-order quadrupolar powder pattern, which can be analyzed to determine quadrupolar coupling constants and asymmetry parameters. The RF power and spinning speed requirements of the original QPASS sequence make it an experimentally demanding technique. A new version of the sequence is demonstrated here and is shown to alleviate many problems associated with the original sequence. New solutions to the determining equations, based on the use of multiple rotor cycles in the QPASS sequence, lead to longer delays between the nine π pulses, provide less chance of pulse overlap, and allow for use of weaker RF field strengths that excite only the central quadrupolar transition. A three-rotor-cycle version of the new experiment is demonstrated on the ¹³⁹La nucleus.     

The propagator of spinless and spinning non-relativistic particles from the BRST-invariant path integral

The BRST-invariant path integral formalism is used in order to calculate the propagator for spinless and spinning non-relativistic particles.     

Holographic forced fluid dynamics in non-relativistic limit

We study the thermodynamics and non-relativistic hydrodynamics of the holographic fluid on a finite cutoff surface in the Gauss–Bonnet gravity. It is shown that the isentropic flow of the fluid is equivalent to a radial component of gravitational field equations. We use the non-relativistic fluid expansion method to study the Einstein–Maxwell-dilaton system with a negative cosmological constant, and obtain the holographic incompressible forced Navier–Stokes equations of the dual fluid at AdS boundary and at a finite cutoff surface, respectively. The concrete forms of external forces are given.     

Inner shell ionization by heavy,charged particles and associated energy loss of the projectile

The process ofL- andM-shell ionization of atoms by heavy, charged particles is analysed in detail by a semiclassical, time-dependent perturbation method. The target electrons are described by non-relativistic hydrogenic wave functions. For the projectile is assumed a well-defined straight-line path. The Coulomb deflection and the screening is partially taken into account. The theoretical values of the total cross section is in reasonable agreement with experimental values. The condition of validity for the semi-classical method is shown to be fulfilled for all non-relativistic projectile energies. The projectile energy loss by ionization is further shown to be of negligible importance for the resolution of magnetic spectrographs used in nuclear structure physics.     

Spontaneous supersymmetry breaking and superconductivity in a non-relativistic model

The conjecture that supersymmetry breaking implies superconductivity is supported by the analysis of a class of supersymmetric non-relativistic models involving only fermions. Here the investigation is extened to a non-relativistic model involving both fermions and bosons, which in a sense is the non-relativistic version of the Wess-Zumino model. A sufficient condition is established for the validity of the conjecture. This condition can be possibly violated at most in a two-dimensional subspace of the three-dimensional space of the coupling constants.     

Initial conditions in non-equilibrium statistical mechanics: I. The generation of solitary waves from discontinuities

Using an iterative projection technique method, a time-evolution equation is derived for the single-particle distribution function. An initial condition with built-in temperature and density discontinuities is used. It is shown that four soliton pairs traveling from the discontinuities may be generated. For the case of a density discontinuity alone, the classical shock tube result is recovered. It is also shown that with a temperature discontinuity, such as may be found in two metals which are brought together, it is possible to generate charged solitary pulses, in addition to the expected flow of electrons across the boundary.     

Double-quantum dipolar recoupling at high magic-angle spinning rates

A full investigation of the possible homonuclear double-quantum recoupling sequences, based on the RN family of sequences with N < or = 20, is given. Several new RN sequences, R16(6)(5), R18(8)(5), and R18(10)(5), were applied at high magic-angle spinning rates and compared with theory. The R18(10)(5) technique can be used to recouple dipolar couplings at spinning rates up to 39 kHz, and the application of the sequence in an INADEQUATE experiment is shown for a spinning rate of 30 kHz.     

An Efficient Algorithm for Truncating Spatial Domain in Modeling Light Scattering by Finite-Difference Technique

The finite-difference time domain technique is one of the most robust and accurate numerical methods for the solution of light scattering by small particles with arbitrary composition and geometry. In practice, this method requires that the spatial domain for the computation of near-field be truncated. An absorbing boundary condition must be imposed in conjunction with this truncation. The performance of this boundary condition is essential to the stability of numerical computations and the reliability of results. In the present study, a new boundary condition, referred to as the mixed T algorithm, has been developed, which is a generalization of the transmitting boundary condition originally developed by Liao and co-workers. The present algorithm does not require spatial interpolation for wave values at interior grid points. In addition, it produces two minima of spurious reflections at small and large incident angles, allowing efficient absorption of the scattered waves at the boundary for large incident angles. When the third-order mixed T algorithm is used, the reflection coefficient of the boundary is less than 1% for incident angles from 0° to about 70°. We find that the numerical instability associated with the transmitting boundary condition is caused by the location-dependent amplitude of outgoing waves in the vicinity of the boundary. For this reason, the mixed T algorithm is stabilized by consistently introducing diffusive coefficients into the boundary equation. When the stabilized algorithm is applied, the near-field within the truncated domain can be computed by using single-precision arithmetic without overflows for more than 10⁵steps in the time-marching iteration. Finally, the new absorbing boundary condition is validated by carrying out numerical experiments involving the propagation of a TM wave excited by a sinusoidal point source, simultaneous simulation of the wave propagation in small and large domains, and the scattering of a TM wave by an infinite circular cylinder.     

An improved covariant treatment of the light mesons

In an earlier paper a covariant version of the two-particle Dirac equation-employing a potential which was a function of the (invariant) proper separation-was used to fit the light meson quark-anti-quark bound states. This paper improves upon that work by introducing a better separation of the equation into internal and external coordinates, and a better separation into angular and radial coordinates. The new eigenvalue which arises from the introduction of hyperspherical harmonics is related to the meson energy in a more rigorous manner than before. As a result, the light meson trajectories can be better fit with fewer free parameters. In particular, the potential now has only Coulomb and linear terms, with no constant term, and current masses are used for the quarks rather than constituent masses. The reduction of the equation to Schrödinger form is discussed. It is shown how the non-relativistic reduction of the linear potential can lead to a constant term in the Schrödinger equation potential, as well as an enhancement of the Coulomb term. The resulting non-relativistic potential is similar to potentials used in successful fits of the charmonium spectrum.     

Variational principles for scattering in the generator coordinate method

The generator coordinate method (GCM) wave function is used as a trial function in a Kohn type variational principle for scattering phase shifts. It is shown that a GCM trial function is a solution of the variational equations if the Hill-Wheeler integral equation is satisfied subject to an appropriate boundary condition. A new method for introducing the scattering boundary condition is presented. There is a uniqueness theorem for the phase shift.