Spin One-half Particles Research Articles

Gravitational moments of spin one-half particles and of topologically massive photons and gravitons in 2+1 dimensions

In 2+1 dimensions we perform a Gordon decomposition of the Lagrangians and currents of spin one-half particles, and of massive photons and gravitons, respectively. We derive and investigate the gravitational moments of these particles. It turns out that, in contrast to the (3+1)-dimensional case, also spinless point particles can carry moments.

SPIN DEPENDENCE OF THE AHARONOV—BOHM EFFECT

The problem of the proper inclusion of spin in Aharonov—Bohm scattering is considered. It is proposed that this should be accomplished by imposing the requirement that all singularities arising from the presence of spin in the associated wave equations be interpreted as limits of physically realizable flux distributions. This leads to results which confirm the usual cross section in the spinless case but imply nontrivial modifications for the scattering of a polarized spin one-half beam. By applying the technique to a calculation of the virial coefficient for a collection of flux carrying spin one-half particles, some severe obstacles to conventional views of the flux as a parameter which interpolates between bosonic and fermionic statistics are shown to occur. Although similar results for the scattering of arbitrary spin particles obtain in the Galilean limit, it is found that when spin one is considered in the context of a relativistic wave equation the singularity structure is too pathological to yield a consistent interpretation. The exact equivalence of the spin one-half Aharonov-Bohm effect to the Aharonov-Casher effect is also demonstrated and corresponding results for polarized beams are presented. Finally, it is shown that the Aharonov-Bohm effect for arbitrary spin in the Galilean limit is the exact solution in the two-particle sector of a Galilean covariant field theory.

CONSTRAINED SUPERFIELDS AND SUPERSYMMETRIC MAGNETIC FIELD SYSTEMS

After Lancaster we examine chiral constraints in N=2 superspace formulation for super-symmetric magnetic field systems. Such odd constraints are connected with the so-called spinorbit coupling procedure of supersymmetrization. We also propose new even constraints for magnetic supersymmetric systems and relate them to the standard procedure enhanced by Witten. These models describing spin-one half particles moving in a plane with a transverse magnetic field are compared and discussed. The cases of a constant magnetic field and of the harmonic oscillator are connected through different correspondences.

Induced gravity for nonzero torsion

Quantum fluctuations of a spin one-half particle in a gravitational background field with nonvanishing torsion are shown to induce again the Einstein-Hilbert term as a long wavelength effective action so that torsion disappears at the classical tree level.

Quantization of classical Grassman spin

We quantize the classical mechanics of anti-commuting Grassman coordinates which transform like Majorana spinors. We evaluate the Grassmann space Feynman path integral to obtain the standard Dirac propagator of a relativistic quantum-mechanical spin one-half particle. In order to obtain our result we impose a natural supersymmetry between ordinary space-time coordinates and the Grassmann coordinates.

Two-body Dirac equations

P. A. M. Dirac took the matrix square root of the Klein-Gordon equation to obtain his relativistic wave equation for a single spin-one-half particle. In this paper, we use Dirac's constraint mechanics and supersymmetry to perform the same operation on the relativistic description of two spinless particles to obtain consistent descriptions of two interacting particles, either or both of which may have spin one-half. The resulting coupled quantum wave equations correctly incorporate relativistic kinematics as well as heavy-particle limits to one-body Dirac or Klein-Gordon equations. The 16-component wave equations for the system of two spin one-half particles separate exactly into four decoupled four-component equations for the analogs of “upper” and “lower” components of the Dirac equation. Perturbative treatment of our equations through 0( α 4) automatically reproduces the appropriate fine structure. Furthermore, like the decoupled forms of Dirac's equation, the two-body versions have spin-dependent pieces that make non-perturbative quantum-mechanical sense. This feature eliminates the need for extra smoothing parameters in the potential or finite particle size in phenomenological applications.

On a possible role of the vector potential in the Einstein-Podolsky-Rosen paradox

A simple hidden-variable model of the Einstein-Podolsky-Rosen experiment with spin one-half particles and Stern-Gerlach magnets is considered. It is shown that a local dependence of the hidden-variable probability distribution on the vector potential of the magnets can, under certain conditions, lead to the same predictions as quantum mechanics.

Is the Experiment of Wu and Shaknov an Empirical Illustration of the Paradox of Einstein, Podolsky and Rosen?

Bohm and Aharonov interpreted the experiment of Wu and Shaknov as an empirical evidence of the paradox of Einstein, Podolsky and Rosen. Peres and Singer tried to deny their interpretation, but they were refuted by the former. It is shown that their reasoning for the interpretation is still unsatisfactory. in a well-known article,!> Einstein, Podolsky and Rosen (hereafter referred to as EPR) pointed out a paradoxical feature concerning the 'completeness' of the current quantum mechanics. Bohm and Aharonov2> (hereafter referred to as BA) formulated the above paradox of EPR, as follows: One considers a pair of spin one-half particles formed somehow in the total spin singlet state and moving freely in opposite directions. Measurement can be made, say by a Stern-Gerlach magnet, on any desired component of the spin cr1 of the particle 1. Suppose that the particle 2 is so remote from the particle 1 that the process of measurement on the latter does not disturb the former. If measurement of (J1z, say, yields the value + 1 or -1, then it can immediately be concluded that (J2z = -1 or + 1, respectively, because of the conservation of the total spin. Thus any desired component of cr2 can be predicted with certainty without in any way disturbing the particle 2. According to EPR all the three independent components of cr2 must be specified simultaneously in a 'complete' theory. Quantum mechanics cannot be a complete theory, because only one component can be specified by the wave function. • Such quantities, components of cr2 for example, as can be predicted with certainty without in any way disturbing the relevant system are called by EPR 'elements of physical reality'.*> EPR required that a 'complete' theory should specify all the elements of physical reality. By the process of the above gedanken experiment only one component of cr2 of each particle 2 can be predicted. The simultaneity of the predictions of all components of cr2 cannot be expected. It may seem at first sight that for each particle only one component of cr2 is the element of physical reality. Nevertheless EPR imposed on a complete theory the simultaneity of the specifica­ tions of all components of cr2 of each particle. This imposition is based on the

Low-energy proton-proton scattering as a test of local hidden-variable theory

E I N 8 T E I N , PODOLSKY and ROSEN (1) (EPR) gave an e~ample of a hypothetical experiment capable of testing certain apparently paradoxical predictions of the curren t quantum theory. BELL (2) proved that local hidden-variable theory cannot contain all of the predictions of quantum mechanics. Bell's proof is based on a Bohm (3) variant of the EPR experiment. WINNER (4) analysed and simplified Bell's argument. BOItM (a), BELL (2) and WIGNER (4) used in their analysis of the EPR experiment the example of a pair of spin-one-half particles formed in the singlet state moving in opposite directions. Photons and not spin-one-half particles, however, have unt i l now been used to test quantum mechanics experimentally because of their greater simplicity. BOHM and A~ARANOV (5) analysed the Wu and Shaknow experiment (~) of positron annihilation into two photons as such a test. CLAUSER, H O R N E , SHIMONY and HOLT (7) proposed an experiment using cascade atomic photons, based on Bell's proof, to test local hiddenvariable theory. P~I~S and S~NGER (s), however, argued some time ago that photons could not test the EPR paradox and suggested instead the use of proton-proton scattering. Bo~a and AHARANOV (9), one the other hand, showed that the argument of PIER, S and SINGER WaS incorrect and that photons could be used to test quantum mechanics. Nevertheless BorI~(1~ emphasized recently that nonmassless spin-onehalf particles would be a better test of local hidden-variable theory than photons. Photons are linear combinations of the normal modes of the electromagnetic field over all space which cannot be localized in space by a Lorentz transformation. The hidden variable of the photon could be associated with the non]ocal electromagnetic field. An experiment using nonmassless spin-one-half particles would be very desirable

Ambiguities of complex phase-shift analysis

It is well known that there exist ambiguities of phase-shift analysis for real potential scattering. For complex potential scattering (complex phase shifts) additional ambiguities arise. We deal with the ambiguities of complex phase-shift analysis made for a definite number of partial waves and given energy. For a given set of complex phase shifts describing elastic scattering of spinless particles we give all other sets of complex phase shifts which correspond to the same total cross section and differential elastic cross section. For a given set of complex phase shifts describing the elastic scattering of spin one-half particles on spinless particles, we give all other sets of phase shifts which correspond to the same total cross section, differential elastic cross section and polarization. Not all ambiguous sets of phase shifts are physically acceptable. Checking with the unitary condition allows one to sift out the unacceptable sets.

Scattering of spin one-half particles from one-dimensional electrostatic potentials

By means of a covariant formalism for the description of spin we investigate the scattering of polarized spin one-half particles from electrostatic potentials that depend on only one space coordinate. We find for an arbitrary potential the scattering intensity to be independent of the polarization of the initial beam. The polarization vector is rotated about an axis normal to the plane of incidence through an angle that only depends on the energy and the angle of incidence of the initial beam.

Polarization of Spin One-Half Particles

The polarization of spin one-half particles may be calculated in two different ways. Either the polarization is evaluated directly by calculating the number of particles polarized in a given direction minus the number polarized in the opposite direction divided by the total number of particles, or with the density matrix approach. The purpose here is to discuss both of the above techniques in an elementary and self-contained fashion. Their equivalence is demonstrated by a calculation of polarization with each method for a general process.

Long-range order in the antiferromagnetic ground state

It is shown that the `paramagnetic' ground-state wave function proposed by Marshall for a system of spin one-half particles interacting by an `antiferromagnetic' Heisenberg interaction has a large sublattice magnetization, comparable with that predicted by spin-wave theory and very close to the result given by perturbation theory. It is argued that the problem of long-range order in such a system is closely related to the problem of long-range order in a system of interacting bosons.

Electron-Nucleon Scattering Cross Section Including All Polarization Correlations

The first-order Born-approximation cross section for the electromagnetic scattering of two nonidentical spin one-half particles is given, including the dependence on arbitrary initial and final spin states of both particles. Both particles are treated relativistically with charge and magnetic-moment interactions.

Problem of a Spin in a Time-Dependent Magnetic Field

The long-standing disagreement between the exact and perturbation solutions for the problem of a spin one-half particle in crossed, time-dependent, magnetic fields is resolved. The resolution is achieved by adapting the perturbation methods given by Krylov, Bogoliubov, and Mitropolskii for classical systems.

Scattering of Polarized Electrons by Polarized Deuterons

The differential cross section for the scattering of arbitrarily polarized charged spin one-half particles by arbitrarily polarized charged spin one-half particles with an anomalous magnetic moment was calculated, including recoil effects. (auth)

A method for the determination of theS-matrix for scattering by a tensor potential

The scattering of two spin one-half particles which are coupled by a tensor force is considered. The usual coupled second-order equations for the radial wave function are transformed into three coupled first-order equations for three real parameters whose asymptotic values determine theS-matrix. The usefulness of such a formulation for numerical computations of theS-matrix is illustrated by considering in detail several simple examples.

The phenomenological description of a relativistic three-particle emission

A relativistic, phenomenological analysis of an arbitrary three-particle emission is made consistent with energy, momentum, and angular momentum conservation. The analysis parallels the general approach to the calculation of a decay rate from an interaction matrix with the unknown matrix elements serving as the arbitrary expansion coefficients. In this manner, the Lorentz invariants of the problem are easily traced. The result is specialized to a localized interaction for an emission of three spin one-half particles. It is shown that, in order to be consistent with Lorentz invariance, the emission must necessarily involve correlations between the momenta of the emitted particles. In the limit of three massless emitted particles, the most general energy spectrum for one of the product particles is calculated. The spectrum thus obtained is identical in form to the parametrized Michel spectra for the electron in muon decay, demonstrating that the Michel spectra have a fundamental origin. It is also shown that merely the added assumption of specific helicities for the emitted particles leads to results for muon decay identical to those obtained from the V- A law.

Note on the Born series

The Born series for the non-relativistic elastic scattering amplitude is investigated for the most elementary type of non-central interaction, a potential between two spin one-half particles for which the departure from spherical symmetry is due to the tensor interaction. It is shown that sufficient conditions for convergence at zero energy are that the potential be static, bounded, of finite range, attractive wherever it does not vanish, and such that there is no resonance at zero energy and no bound state at any energy. Convergence is also obtained if the sign of the potential is reversed.

Low-Field Nuclear Magnetic Resonance of Coupled Spin—One-Half Particles

First Page