Quantization of Nonstandard Hamiltonian Systems

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of the quantum theory. A spin-1/2 system is taken as an example in which all the steps can be completed. It is shown that the geometry of the quantum theory imposes restrictions on the physically allowed nonstandard quantum theories.Comment: Revtex file, 23 pages, no figure

Twistors, special relativity, conformal symmetry and minimal coupling - a review

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincare scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled, Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so called Thomas Bergman Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything else in the papper) on page 23 delete

Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron

The spectroscopic binary system Gl 375. I. Orbital parameters and chromospheric activity

We study the spectroscopic binary system Gl 375. We employ medium resolution echelle spectra obtained at the 2.15 m telescope at the Argentinian observatory CASLEO and photometric observations obtained from the ASAS database. We separate the composite spectra into those corresponding to both components. The separated spectra allow us to confirm that the spectral types of both components are similar (dMe3.5) and to obtain precise measurements of the orbital period (P = 1.87844 days), minimum masses (M_1 sin^3 i = 0.35 M_sun and M_2 sin^3 i =0.33 M_sun) and other orbital parameters. The photometric observations exhibit a sinusoidal variation with the same period as the orbital period. We interpret this as signs of active regions carried along with rotation in a tidally synchronized system, and study the evolution of the amplitude of the modulation in longer timescales. Together with the mean magnitude, the modulation exhibits a roughly cyclic variation with a period of around 800 days. This periodicity is also found in the flux of the Ca II K lines of both components, which seem to be in phase. The periodic changes in the three observables are interpreted as a sign of a stellar activity cycle. Both components appear to be in phase, which implies that they are magnetically connected. The measured cycle of approximately 2.2 years (800 days) is consistent with previous determinations of activity cycles in similar stars.Comment: 10 pages, including 11 figures and 3 tables. Accepted for publication in Astronomy & Astrophysic

On spin-1 massive particles coupled to a Chern-Simons field

We study spin one particles interacting through a Chern-Simons field. In the Born approximation, we calculate the two body scattering amplitude considering three possible ways to introduce the interaction: (a) a Proca like model minimally coupled to a Chern-Simons field, (b) the model obtained from (a) by replacing the Proca's mass by a Chern-Simons term and (c) a complex Maxwell-Chern-Simons model minimally coupled to a Chern-Simons field. In the low energy regime the results show similarities with the Aharonov-Bohm scattering for spin 1/2 particles. We discuss the one loop renormalization program for the Proca's model. In spite of the bad ultraviolet behavior of the matter field propagator, we show that, up to one loop the model is power counting renormalizable thanks to the Ward identities satisfied by the interaction vertices.Comment: 14 pages, 5 figures, revte

Spacetime dynamics of spinning particles - exact electromagnetic analogies

We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers," a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.Comment: 32+11 pages, 5 figures. Edited and further improved version, with new Section C.2 unveiling analogies for arbitrary spin conditions, and new Sec. 3.2.3 in the Supplement making connection to the post-Newtonian approximation; former Sec. III.B.4 and Appendix C moved to the (reshuffled) Supplement; references updated. The Supplement is provided in ancillary file. Matches the final published versio

Generalized Euler Angle Paramterization for SU(N)

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.Comment: 36 pages, no figures; added qubit/qutrit work, corrected minor definition problems and clarified Haar measure derivation. To be published in J. Phys. A: Math. and Ge

Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix formulation is given for decoherence effects on the Stokes parameters, and a possible experiment is proposed. It is shown also that this Lorentz-group formalism leads to optical filters with a symmetry property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.

Rotation and Spin in Physics

We delineate the role of rotation and spin in physics, discussing in order Newtonian classical physics, special relativity, quantum mechanics, quantum electrodynamics and general relativity. In the latter case, we discuss the generalization of the Kepler formula to post-Newtonian order $(c^{-2}$) including spin effects and two-body effects. Experiments which verify the theoretical results for general relativistic spin-orbit effects are discussed as well as efforts being made to verify the spin-spin effects

Chedoke Arm and Hand Activity Inventory-9 (CAHAI-9): Perceived clinical utility within 14 days of stroke

Purpose: The Chedoke Arm and Hand Activity Inventory-9 (CAHAI-9) is an activity-based assessment developed to include relevant functional tasks and to be sensitive to clinically important changes in upper limb function. The aim of this study was to explore both therapists' and clients' views on the clinical utility of CAHAI-9 within 14 days of stroke. Method: Twenty-one occupational therapists actively working in stroke settings were recruited by convenience sampling from 8 hospitals and participated in semistructured focus groups. Five clients within 14 days of stroke were recruited by consecutive sampling from 1 metropolitan hospital and participated in structured individual interviews. The transcripts were analyzed thematically. Results: Six themes emerged from the focus groups and interviews: collecting information, decisions regarding client suitability, administration and scoring, organizational demands, raising awareness, and clients' perceptions of CAHAI-9 utility. All therapists agreed CAHAI-9 was suited for the stroke population and assisted identification of client abilities or difficulties within functional contexts. Opinions varied as to whether CAHAI-9 should be routinely administered with clients who had mild and severe upper limb deficits, but therapists agreed it was appropriate for clients with moderate deficits. Therapists made suggestions regarding refinement of the scoring and training to increase utility. All clients with stroke felt that the assessment provided reassurance regarding their recovery. Conclusion: The findings indicate that CAHAI-9 shows promise as an upper limb ability assessment for clients within 14 days of stroke