Off-Diagonal Long-Range Order, Restricted Gauge Transformations, and Aharonov-Bohm Effect in Conductors

The Hamiltonian describing a conductor surrounding an external magnetic field contains a nonvanishing vector potential in the volume accessible to the electrons and nuclei of which the conductor is made. That vector potential cannot be removed by a gauge transformation. Nevertheless, a macroscopic normal conductor can experience no Aharonov-Bohm effect. That is proved by assuming only that a normal conductor lacks off-diagonal long-range order (ODLRO). Then by restricting the Hilbert space to density matrices which lack ODLRO, it is possible to introduce a restricted gauge transformation that removes the interaction of the conductor with the vector potential.Comment: Editing errors are corrected. One was slightly misleadin

Spin and Statistics in Galilean Covariant Field Theory

The existence of a possible connection between spin and statistics is explored within the framework of Galilean covariant field theory. To this end fields of arbitrary spin are constructed and admissible interaction terms introduced. By explicitly solving such a model in the two particle sector it is shown that no spin and statistics connection can be established

Against a proposed alternative explanation of the Aharonov-Bohm effect

The Aharonov-Bohm effect is understood to demonstrate that the Maxwell fields can act nonlocally in some situations. However it has been suggested from time to time that the AB effect is somehow a consequence of a local classical electromagnetic field phenomenon involving energy that is temporarily stored in the overlap between the external field and the field of which the beam particle is the source. That idea was shown in the past not to work for some models of the source of the external field. Here a more general proof is presented for the magnetic AB effect to show that the overlap energy is always compensated by another contribution to the energy of the magnetic field in such a way that the sum of the two is independent of the external flux. Therefore no such mechanism can underlie the Aharonov-Bohm effect.Comment: 7 pages, 1 figur

Topology, Locality, and Aharonov-Bohm Effect with Neutrons

Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local torque in the magnetic field. We note that the same remarks apply to the Aharonov-Casher effect.Comment: 9 page

A New Class of Path Equations in AP-Geometry

In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation to the geodesic one. If the basic vector of the AP-geometry is considered as playing the role of the electromagnetic potential, as done in a previous work, then the second term (of the extra terms) will represent Lorentz force while the fourth term gives a direct effect of the electromagnetic potential on the motion of the charged particle. This last term may give rise to an effect similar to the Aharanov-Bohm effect. It is to be considered that all extra terms will vanish if the space-time used is torsion-less.Comment: 11 pages, LaTeX fil

Task planning and control synthesis for robotic manipulation in space applications

Space-based robotic systems for diagnosis, repair and assembly of systems will require new techniques of planning and manipulation to accomplish these complex tasks. Results of work in assembly task representation, discrete task planning, and control synthesis which provide a design environment for flexible assembly systems in manufacturing applications, and which extend to planning of manipulatiuon operations in unstructured environments are summarized. Assembly planning is carried out using the AND/OR graph representation which encompasses all possible partial orders of operations and may be used to plan assembly sequences. Discrete task planning uses the configuration map which facilitates search over a space of discrete operations parameters in sequential operations in order to achieve required goals in the space of bounded configuration sets

Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts

The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin Lagrangian is used to analyze the electromagnetic behavior of the model magnetic moment (composed of two oppositely charged particles of different mass in an initially circular orbit) interacting with a passing point charge. The changing mangetic moment is found to put a force back on a passing charge; this force is of order 1/c^2 and depends upon the magnitude of the magnetic moment. It is suggested that in the limit of a multiparticle magnetic toroid, the electric fields of the passing charge are screened out of the body of the magnet while the magnetic fields penetrate into the magnet. This is consistent with our understanding of the penetration of electromagnetic velocity fields into ohmic conductors. Conservation laws are discussed. The work corresponds to a classical electromagnetic analysis of the interaction which is basic to understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase shifts and represents a refutation of the suggestions of Aharonov, Pearle, and Vaidman.Comment: 33 page

Remarks on the Configuration Space Approach to Spin-Statistics

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.Comment: 18 page

Non-dipole angular anisotropy parameters of semi-filled shell atoms

We present the results of calculations of outer shell non-dipole angular anisotropy parameters for semi-filled shell atoms in the Hartree-Fock (HF) one-electron approximation and with account of inter-electron correlations in the frame of the Spin Polarized Random Phase Approximation with Exchange (SP RPAE). We demonstrate for the first time that this characteristic of photoionization process is essentially sensitive to the fact whether the photoelectron has the same or opposite spin orientation to that of the semi-filled shell.Comment: 15 pages, 8 figure