QCD strings with spinning quarks

We construct a consistent action for a massive spinning quark on the end of a QCD string that leads to pure Thomas precession of the quark's spin. The string action is modified by the addition of Grassmann degrees of freedom to the string such that the equations of motion for the quark spin follow from boundary conditions, just as do those for the quark's position.Comment: REVTeX4, 10 pages, no figure

Relativistic Generalization of the Gamow Factor for Fermion Pair Production or Annihilation

In the production or annihilation of a pair of fermions, the initial-state or final-state interactions often lead to significant effects on the reaction cross sections. For Coulomb-type interactions, the Gamow factor has been traditionally used to take into account these effects. However the Gamow factor needs to be modified when the magnitude of the coupling constant or the relative velocity of two particles increases. We obtain the relativistic generalization of the Gamow factor in terms of the overlap of the Feynman amplitude with the relativistic wave function of two fermions with an attractive Coulomb-type interaction. An explicit form of the corrective factor is presented for the spin-singlet S-wave state. While the corrective factor approaches the Gamow factor in the non-relativistic limit, we found that the Gamow factor significantly over-estimates the effects when the coupling constant or the velocity is large.Comment: 16 pages, 4 figures in LaTe

Tensionless String in the Notoph Background

We study the interaction between a tensionless (null) string and an antisymmetric background field B_{ab} using a 2-component spinor formalism. A geometric condition for the absence of such an interaction is formulated. We show that only one gauge-invariant degree of freedom of the field B_{ab} does not satisfy this condition. Identification of this degree of freedom with the notoph field \phi of Ogievetskii-Polubarinov-Kalb-Ramond is suggested. Application of a two-component spinor formalism allows us a reduction of the complete system of non-linear partial differential equations and constraints governing the interacting null string dynamics to a system of linear differential equations for the basis spinors of the spin-frame. We find that total effect of the interaction is contained in a single derivation coefficient which is identified with the notoph field.Comment: 15 pages, no figures, RevTeX 3.

Perspectives on Continental Rifting Processes From Spatiotemporal Patterns of Faulting and Magmatism in the Rio Grande Rift, USA

Analysis of spatiotemporal patterns of faulting and magmatism in the Rio Grande rift (RGR) in New Mexico and Colorado, USA, yields insights into continental rift processes, extension accommodation mechanisms, and rift evolution models. We combine new apatite (U‐Th‐Sm)/He and zircon (U‐Th)/He thermochronometric data with previously published thermochronometric data to assess the timing of fault initiation, magnitudes of fault exhumation, and growth and linkage patterns of rift faults. Thermal history modeling of these data reveals contemporaneous rift initiation at ca. 25 Ma in both the northern and southern RGR with continued fault initiation, growth, and linkage progressing from ca. 25 to ca. 15 Ma. The central RGR, however, shows no evidence of Cenozoic fault‐related exhumation as observed with thermochronometry and instead reveals extension accommodated through Late Cenozoic magmatic injection. Furthermore, faulting in the northern and southern RGR occurs along an approximately north‐south strike, whereas magmatism in the central RGR occurs along the northeast to southwest trending Jemez lineament. Differences in deformation orientation and rift accommodation along strike appear to be related to crustal and lithospheric properties, suggesting that rift structure and geometry are at least partly controlled by inherited lithospheric‐scale architecture. We propose an evolutionary model for the RGR that involves initiation of fault‐accommodated extension by oblique strain followed by block rotation of the Colorado Plateau, where extension in the RGR is accommodated by faulting (southern and northern RGR) and magmatism (central RGR). This study highlights different processes related to initiation, geometry, extension accommodation, and overall development of continental rifts.Plain Language SummaryWe identify patterns of faulting and volcanism in the Rio Grande rift (RGR) in the western United States to better understand how continental rifts evolve. Using methods for documenting rock cooling ages (thermochronology), we determined that rifting began around 25 million years ago (Ma) in both the northern and southern RGR. Rift faults continued to develop and grow for another 10 to 15 million years. The central RGR, however, shows that rift extension occurred through volcanic activity both as eruptions at the surface and as magma injection below the surface since ~15 Ma. Interestingly, RGR faulting in the north and south parts of the rift occurs on a north‐south line, while volcanism in the central RGR is along a northeast to southwest line. The differences in the location and orientation of faulting and volcanic activity may be related to the thickness of the lithosphere beneath different parts of the rift. Using these patterns of faulting and magmatism, we propose the RGR evolved through a combination of (1) oblique strain—extension diagonal to the rift and (2) block rotation—where the Colorado Plateau is the rotating block. This detailed study highlights different processes related to the accommodation of extension and the overall development of continental rifts.Key PointsInitiation of the Rio Grande rift appears to be synchronous ~25 Ma and does not support a northward propagation modelExtension is accommodated by faulting in the northern and southern Rio Grande rift and by magmatic injection in the central Rio Grande riftDifferent rift accommodation mechanisms may be controlled by preexisting weaknesses and lithospheric properties (i.e., thickness)Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152704/1/tect21226.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152704/2/wrcr21226-sup-00001-2019TC005635-SI.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152704/3/tect21226_am.pd

The Relativistic N-body Problem in a Separable Two-Body Basis

We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body Hamiltonian is relativistically covariant. It can be easily separated in terms of the center-of-mass and the relative motion of any two-body subsystem. It can also be separated into an unperturbed Hamiltonian with a residual interaction. In a system of two-body composite particles, the solutions of the unperturbed Hamiltonian are relativistic two-body internal states, each of which can be obtained by solving a relativistic Schr\"odinger-like equation. The resultant two-body wave functions can be used as basis states to evaluate reaction matrix elements in the general N-body problem. We prove a relativistic version of the post-prior equivalence which guarantees a unique evaluation of the reaction matrix element, independent of the ways of separating the Hamiltonian into unperturbed and residual interactions. Since an arbitrary reaction matrix element involves composite particles in motion, we show explicitly how such matrix elements can be evaluated in terms of the wave functions of the composite particles and the relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe

Environmental justice and conceptions of the green economy

Green economy has become one of the most fashionable terms in global environmental public policy discussions and forums. Despite this popularity, and its being selected as one of the organizing themes of the United Nations Rio+20 Conference in Brazil, June 2012, its prospects as an effective mobilization tool for global environmental sustainability scholarship and practice remains unclear. A major reason for this is that much like its precursor concepts such as environmental sustainability and sustainable development, green economy is a woolly concept which lends itself to many interpretations. Hence, rather than resolve long-standing controversies, green economy merely reinvigorates existing debates over the visions, actors and policies best suited to secure a more sustainable future for all. In this review article, we aim to fill an important gap in scholarship by suggesting various ways in which green economy may be organized and synthesized as a concept, and especially in terms of its relationship with the idea of social and environmental justice. Accordingly, we offer a systemization of possible interpretations of green economy mapped onto a synthesis of existing typologies of environmental justice. This classification provides the context for future analysis of which, and how, various notions of green economy link with various conceptions of justice