REPLY TO HEP-PH/0211241 "On the extra factor of two in the phase of neutrino oscillations"

Arguments continue to appear in the literature concerning the validity of the standard oscillation formula. We point out some misunderstandings and try to explain in simple terms our viewpoint.Comment: 4 pages [1 colored LaTex-fig], AMS-Te

Wave packets and quantum oscillations

We give a detailed analysis of the oscillation formula within the context of the wave packet formalism. Particular attention is made to insure flavor eigenstate creation in the physical cases (Delta p not equal 0). This requirement imposes non instantaneous particle creation in all frames. It is shown that the standard formula is not only exact when the mass wave packets have the same velocity, but it is a good approximation when minimal slippage occurs. For more general situations the oscillation formula contains additional arbitrary parameters, which allows for the unknown form of the wave packet envelope.Comment: 15 pages [8 figs], AMS-Te

Commutators as Powers in Free Products of Groups

The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified.Comment: AMS-LaTex, 6 pages, no figure

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Quaternionic potentials in non-relativistic quantum mechanics

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te

Potential Scattering in Dirac Field Theory

We develop the potential scattering of a spinor within the context of perturbation field theory. As an application, we reproduce, up to second order in the potential, the diffusion results for a potential barrier of quantum mechanics. An immediate consequence is a simple generalization to arbitrary potential forms, a feature not possible in quantum mechanics.Comment: 7 page

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

Mutual Inductance Route to Paramagnetic Meissner Effect in 2D Josephson Junction Arrays

We simulate two-dimensional Josephson junction arrays, including full mutual- inductance effects, as they are cooled below the transition temperature in a magnetic field. We show numerical simulations of the array magnetization as a function of position, as detected by a scanning SQUID which is placed at a fixed height above the array. The calculated magnetization images show striking agreement with the experimental images obtained by A. Nielsen et al. The average array magnetization is found to be paramagnetic for many values of the applied field, confirming that paramagnetism can arise from magnetic screening in multiply-connected superconductors without the presence of d-wave superconductivity.Comment: REVTeX 3.1, 5 pages, 5 figure

Dirac Equation Studies in the Tunnelling Energy Zone

We investigate the tunnelling zone V0 < E < V0+m for a one-dimensional potential within the Dirac equation. We find the appearance of superluminal transit times akin to the Hartman effect.Comment: 12 pages, 4 figure