Perturbative Expansion in the Galilean Invariant Spin One-Half Chern-Simons Field Theory

A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-1/2 fields of distinct masses M and M'. A method for the construction of states containing N particles of mass M and N' particles of mass M' is given which is subsequently used to display equivalence to the spin-1/2 Aharonov-Bohm effect in the N = N' =1 sector of the model. The latter is then studied in perturbation theory to determine whether there are divergences in the fourth order (one loop) diagram. It is found that the contribution of that order is finite (and vanishing) for the case of parallel spin projections while the antiparallel case displays divergences which are known to characterize the spin zero case in field theory as well as in quantum mechanics.Comment: 14 pages LaTeX, including 2 figures using eps

Spinning test particles and clock effect in Kerr spacetime

We study the motion of spinning test particles in Kerr spacetime using the Mathisson-Papapetrou equations; we impose different supplementary conditions among the well known Corinaldesi-Papapetrou, Pirani and Tulczyjew's and analyze their physical implications in order to decide which is the most natural to use. We find that if the particle's center of mass world line, namely the one chosen for the multipole reduction, is a spatially circular orbit (sustained by the tidal forces due to the spin) then the generalized momentum $P$ of the test particle is also tangent to a spatially circular orbit intersecting the center of mass line at a point. There exists one such orbit for each point of the center of mass line where they intersect; although fictitious, these orbits are essential to define the properties of the spinning particle along its physical motion. In the small spin limit, the particle's orbit is almost a geodesic and the difference of its angular velocity with respect to the geodesic value can be of arbitrary sign, corresponding to the spin-up and spin-down possible alignment along the z-axis. We also find that the choice of the supplementary conditions leads to clock effects of substantially different magnitude. In fact, for co-rotating and counter-rotating particles having the same spin magnitude and orientation, the gravitomagnetic clock effect induced by the background metric can be magnified or inhibited and even suppressed by the contribution of the individual particle's spin. Quite surprisingly this contribution can be itself made vanishing leading to a clock effect undistiguishable from that of non spinning particles. The results of our analysis can be observationally tested.Comment: IOP macros, eps figures n. 12, to appear on Classical and Quantum Gravity, 200

Perturbative Analysis of Nonabelian Aharonov-Bohm Scattering

We perform a perturbative analysis of the nonabelian Aharonov-Bohm problem to one loop in a field theoretic framework, and show the necessity of contact interactions for renormalizability of perturbation theory. Moreover at critical values of the contact interaction strength the theory is finite and preserves classical conformal invariance.Comment: 12 pages in LaTeX, uses epsf.sty, 5 uuencoded Postscript figures sent separately. MIT-CTP-228

Innermost Stable Circular Orbit of a Spinning Particle in Kerr Spacetime

We study stability of a circular orbit of a spinning test particle in a Kerr spacetime. We find that some of the circular orbits become unstable in the direction perpendicular to the equatorial plane, although the orbits are still stable in the radial direction. Then for the large spin case ($S < \sim O(1)), the innermost stable circular orbit (ISCO) appears before the minimum of the effective potential in the equatorial plane disappears. This changes the radius of ISCO and then the frequency of the last circular orbit.Comment: 25 pages including 8 figure

Spinning test particles and clock effect in Schwarzschild spacetime

We study the behaviour of spinning test particles in the Schwarzschild spacetime. Using Mathisson-Papapetrou equations of motion we confine our attention to spatially circular orbits and search for observable effects which could eventually discriminate among the standard supplementary conditions namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the world line chosen for the multipole reduction and whose unit tangent we denote as $U$ is a circular orbit then also the generalized momentum $P$ of the spinning test particle is tangent to a circular orbit even though $P$ and $U$ are not parallel four-vectors. These orbits are shown to exist because the spin induced tidal forces provide the required acceleration no matter what supplementary condition we select. Of course, in the limit of a small spin the particle's orbit is close of being a circular geodesic and the (small) deviation of the angular velocities from the geodesic values can be of an arbitrary sign, corresponding to the possible spin-up and spin-down alignment to the z-axis. When two spinning particles orbit around a gravitating source in opposite directions, they make one loop with respect to a given static observer with different arrival times. This difference is termed clock effect. We find that a nonzero gravitomagnetic clock effect appears for oppositely orbiting both spin-up or spin-down particles even in the Schwarzschild spacetime. This allows us to establish a formal analogy with the case of (spin-less) geodesics on the equatorial plane of the Kerr spacetime. This result can be verified experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum gravity, 200

Atypical presentation of acute idiopathic megacolon in a 14-year-old patient

In clinical practice the term "megacolon" is used to indicate a marked dilatation of the cecum and the sigmoid colon (>12 and 6.5 cm, respectively) (1). From a clinical standpoint, a megacolon can be classified as chronic or acute depending on its clinical presentation. Chronic megacolon typically refers to a congenital disorder in which the enteric nervous system (ENS) supplying the colon does not develop properly, thereby leaving the distal segments of the viscus without myenteric and submucosal ganglia (i.e. Hirschsprung's disease) (2). Other cases of non-aganglionic chronic megacolon can be secondary to variety of conditions such as Chagas' disease and neurodegenerative diseases (e.g. Parkinson's and Alzheimer's diseases), leading to or associated with ENS abnormalities (3). The acute form of megacolon, also referred to as Ogilvie's syndrome, is characterized by a predominant involvement of the cecum and right colon usually affecting elderly patients undergoing surgery (e.g. orthopedic procedures) or taking medications altering gut motility (e.g. opioids or antidepressants) (4). Some forms of acute megacolon, however, can be idiopathic in origin since no underlying etiology can be identified. Patients with acute idiopathic megacolon usually have a longstanding history of constipation, often accompanied by laxative abuse, and their clinical presentation is characterized by abdominal distension and severe pain with radiological evidence of stool impacted in the colon and rectum (1, 4). The case herein reported represents an unusual form of acute idiopathic megacolon characterized by massive descending and sigmoid colon distension complicated with a volvulus in a 14-year-old boy with no Hirschsprung's disease. In addition, just to increase the peculiarity of this case report, the patient had an unremarkable clinical record, and never suffered from chronic constipation in the past

On the scattering amplitude in the Aharonov-Bohm gauge field

A general expression for the scattering amplitude of nonrelativistic spinless particles in the Aharonov-Bohm gauge potential is obtained within the time independent formalism. The result is valid also in the backward and forward directions as well as for any choice of the boundary conditions on the wave function at the flux tube position.Comment: 18 pages, plain TE

Radiative Corrections to the Aharonov-Bohm Scattering

We consider the scattering of relativistic electrons from a thin magnetic flux tube and perturbatively calculate the order $\alpha$, radiative correction, to the first order Born approximation. We show also that the second order Born amplitude vanishes, and obtain a finite inclusive cross section for the one-body scattering which incorporates soft photon bremsstrahlung effects. Moreover, we determine the radiatively corrected Aharonov-Bohm potential and, in particular, verify that an induced magnetic field is generated outside of the flux tube.Comment: 14 pages, revtex, 3 figure