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

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

Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.Comment: 8 page

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

Resonant laser tunnelling

We propose an experiment involving a gaussian laser tunneling through a twin barrier dielectric structure. Of particular interest are the conditions upon the incident angle for resonance to occur. We provide some numerical calculations for a particular choice of laser wave length and dielectric refractive index which confirm our expectations.Comment: 15 pages, 6 figure

The Asymptotic Giant Branch and the Tip of the Red Giant Branch as Probes of Star Formation History: The Nearby Dwarf Irregular Galaxy KKH 98

We investigate the utility of the asymptotic giant branch (AGB) and the red giant branch (RGB) as probes of the star formation history (SFH) of the nearby (D=2.5 Mpc) dwarf irregular galaxy, KKH 98. Near-infrared (IR) Keck Laser Guide Star Adaptive Optics (AO) images resolve 592 IR bright stars reaching over 1 magnitude below the Tip of the Red Giant Branch. Significantly deeper optical (F475W and F814W) Hubble Space Telescope images of the same field contain over 2500 stars, reaching to the Red Clump and the Main Sequence turn-off for 0.5 Gyr old populations. Compared to the optical color magnitude diagram (CMD), the near-IR CMD shows significantly tighter AGB sequences, providing a good probe of the intermediate age (0.5 - 5 Gyr) populations. We match observed CMDs with stellar evolution models to recover the SFH of KKH 98. On average, the galaxy has experienced relatively constant low-level star formation (5 x 10^-4 Mo yr^-1) for much of cosmic time. Except for the youngest main sequence populations (age < 0.1 Gyr), which are typically fainter than the AO data flux limit, the SFH estimated from the the 592 IR bright stars is a reasonable match to that derived from the much larger optical data set. Differences between the optical and IR derived SFHs for 0.1 - 1 Gyr populations suggest that current stellar evolution models may be over-producing the AGB by as much as a factor of three in this galaxy. At the depth of the AO data, the IR luminous stars are not crowded. Therefore these techniques can potentially be used to determine the stellar populations of galaxies at significantly further distances.Comment: 15 pages, 14 figs, accepted for publication in Ap

A Magellanic Origin for the Warp of the Galaxy

We show that a Magellanic Cloud origin for the warp of the Milky Way can explain most quantitative features of the outer HI layer recently identified by Levine, Blitz & Heiles (2005). We construct a model similar to that of Weinberg (1998) that produces distortions in the dark matter halo, and we calculate the combined effect of these dark-halo distortions and the direct tidal forcing by the Magellanic Clouds on the disk warp in the linear regime. The interaction of the dark matter halo with the disk and resonances between the orbit of the Clouds and the disk account for the large amplitudes observed for the vertical m=0,1,2 harmonics. The observations lead to six constraints on warp forcing mechanisms and our model reasonably approximates all six. The disk is shown to be very dynamic, constantly changing its shape as the Clouds proceed along their orbit. We discuss the challenges to MOND placed by the observations.Comment: 4 pages, 3 figures, submitted to ApJ Letters. Additional graphics, 3d visualizations and movies available at http://www.astro.umass.edu/~weinberg/lm

The Abominable Traffic: The Abolition Movement and Emotions

It is obvious that emotions play an important role in social movement campaigns. Strangely enough, however, studies of social movements do not pay much attention to emotions nor do they give them an appropriate place in social movement theory. As Hunt and Benford contend, this overly rationalistic theory urgently needs a 'dramaturgical infusion'. In this paper we follow their lead. In it we explore historical studies of the first public campaign of the eighteenth-century abolition movement in Great Britain to shed light on the role of emotions in movement discourses. Following Hochschild we assume that each society and each culture has its unique emotional dictionary, which defines what is and isn't, and its emotional bible, which defines what one should and should not feel in a given context." In social movement campaigns, actors employ the emotional repertoires of their society in order to express their indignation, to evoke emotional feelings in the audiences they address and thus put pressure on authorities to change their policies. The analysis of the first public campaign of the British abolition movement shows that the feelings about the abolition of the slave trade often ran high. Both the abolitionists and their opponents used a great variety of emotion signs as means to communicate with the world of politics and with society at large. The analysis reveals that four variables determined the degree of emotionality in the abolition discourse. First, the nature of the cause, i.e., abolition of the slave trade. Particularly, the degree of inequality involved in slavery determined the level of moral indignation that fueled the abolition campaign. Second, the strategic-instrumental choices of the leading movement actors when to use emotional arguments and when to revert to more 'business-like' pleas. Third, the cultural climate in which a campaign takes place. In this case the cultural climate of the late eighteenth century contributed much to the emotionality of the abolition discourse. Fourth, the emotional tone of the discourses in extant critical communities, i.e., in the debates initiated by critical thinkers about a topic. In the case of abolition, the pre-dominantly emotional debate that took place within religious, particularly Evangelical, circles did much to make the abolition discourse a heated one. The analysis shows that emotions are essential to get a movement started and to keep it going. They therefore deserve scholarly attention in their own right and must not be taken granted as folklore of movement campaigns