The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the potential (i.e. A μ dx μ ) and the field (i.e. 1 2 F μν dσ μν ) forms of the Aharonov-Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space-time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov-Bohm effect could be observed.

Hiickel model with one-s-electron per atom is used to study the geometries and electroniC structures of clusters of 9 to 22 atoms. '!\vo different optimization schemes for obtaining the ground states are used; (i) minimization of., an approximate Hiickel ground state energy starting from a random geometry and (ii) simulated annealing. Both methods give similar and new ground state geometries for clusters with 10 to. 14 atoms. All clusters with more than 10 atoms will be distorted if the bond distance is allowed to vary ±5.5%. The ground states of clusters with atoms 10, 11, 12, and 14 are found to have the N = 9 cluster as the basic building block, whereas the, N = 13 c1usteris a distorted cuboctahedron. As a general trend, the deformation of clusters i~creases from atom number B to 14 and shrinks again from 15 to'20 atoms, in accordance with jeIiium m<;>del results. .These constraints make the Hiickel model difficult. The simpiest model is to require that all nearest neighbor 'distances :are the same (rmin=rmax). This is a hard sphere model, where only the touching spheres are nearest neighbors. This model

The standard procedure for making a global phase symmetry local involves the introduction of a rank 1, vector field in the definition of the covariant derivative. Here it is shown that it is possible to gauge a phase symmetry using fields of various ranks. In contrast to other formulations of higher rank gauge fields we begin with the coupling of the gauge field to some matter field, and then derive the gauge invariant, field strength tensor. Some of these gauge theories are similar to general relativity in that their covariant derivatives involve derivatives of the rank n gauge field rather than just the gauge field. For general relativity the covariant derivative involves the Christoffel symbols which are written in terms of derivatives of the metric tensor. Many (but not all) of the Lagrangians that we find for these higher rank gauge theories lead to nonrenormalizable quantum theories which is also similar to general relativity.Comment: References adde

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