104 research outputs found
The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics
We examine some of the subtleties inherent in formulating a theory of spinors
on a manifold with a smooth degenerate metric. We concentrate on the case where
the metric is singular on a hypersurface that partitions the manifold into
Lorentzian and Euclidean domains. We introduce the notion of a complex spinor
fibration to make precise the meaning of continuity of a spinor field and give
an expression for the components of a local spinor connection that is valid in
the absence of a frame of local orthonormal vectors. These considerations
enable one to construct a Dirac equation for the discussion of the behavior of
spinors in the vicinity of the metric degeneracy. We conclude that the theory
contains more freedom than the spacetime Dirac theory and we discuss some of
the implications of this for the continuity of conserved currents.Comment: 24 pages, LaTeX (RevTeX 3.0, no figures), To appear in J. Math. Phy
Finite action Yang-Mills solutions on the group manifold
We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable one to construct solutions of the Yang-Mills equations on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3)
Casinos in context : the impacts of stand-alone casino development on urban neighborhoods
Thesis (M.C.P.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 2007.Includes bibliographical references (p. 169-174).As the stigma of gambling fades and governments seek more sources of revenue the urban casino is becoming more common. Many of these are legalized to operate with limited competition in their state, standing alone in their respective city. while the general, diffuse impacts of casinos have been well studied, the paucity of casinos in urban settings has left a gap in the understanding of how stand-alone casinos affect their urban context. This thesis seeks to fill this gap by analyzing three of the oldest stand-alone urban casinos in the United States: Harrah's Casino in Joliet, Harrah's Casino in New Orleans, and Greektown Casino in Detroit. The thesis analyzes the impact of each of these casinos through the lens of five categories of impact: urban design of the neighborhood, city investment, real estate development, street-level commerce, and the residential community. The resulting analysis finds that casinos tend to be insular entities that do not impact much outside their own footprint. Their greatest potential for external impacts is an ability to act as an anchor for street-level commerce in a neighborhood if designed properly, a trend that has been observed for some time in resort communities with fake interior streets. The essay concludes with recommendations on how a city might engender a similar phenomenon.by Luke J. Schray.M.C.P
Quaternionic Spin
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic
2-component spinors, leading to a formalism which treats both massive and
massless particles on an equal footing. The resulting unified description has
the correct particle spectrum to be a generation of leptons, with the correct
number of spin/helicity states. Furthermore, precisely three such generations
naturally combine into an octonionic description of the 10-dimensional massless
Dirac equation, as discussed in previous work.Comment: LaTeX2e, 15 pages, 1 PS figure; to appear in Clifford '99 proceeding
Formulation of polylactide-co-glycolic acid nanospheres for encapsulation and sustained release of poly(ethylene imine)-poly(ethylene glycol) copolymers complexed to oligonucleotides
Antisense oligonucleotides (AOs) have been shown to induce dystrophin expression in muscles cells of patients with Duchenne Muscular Dystrophy (DMD) and in the mdx mouse, the murine model of DMD. However, ineffective delivery of AOs limits their therapeutic potential. Copolymers of cationic poly(ethylene imine) (PEI) and non-ionic poly(ethylene glycol) (PEG) form stable nanoparticles when complexed with AOs, but the positive surface charge on the resultant PEG-PEI-AO nanoparticles limits their biodistribution. We adapted a modified double emulsion procedure for encapsulating PEG-PEI-AO polyplexes into degradable polylactide-co-glycolic acid (PLGA) nanospheres. Formulation parameters were varied including PLGA molecular weight, ester end-capping, and sonication energy/volume. Our results showed successful encapsulation of PEG-PEI-AO within PLGA nanospheres with average diameters ranging from 215 to 240 nm. Encapsulation efficiency ranged from 60 to 100%, and zeta potential measurements confirmed shielding of the PEG-PEI-AO cationic charge. Kinetic measurements of 17 kDa PLGA showed a rapid burst release of about 20% of the PEG-PEI-AO, followed by sustained release of up to 65% over three weeks. To evaluate functionality, PEG-PEI-AO polyplexes were loaded into PLGA nanospheres using an AO that is known to induce dystrophin expression in dystrophic mdx mice. Intramuscular injections of this compound into mdx mice resulted in over 300 dystrophin-positive muscle fibers distributed throughout the muscle cross-sections, approximately 3.4 times greater than for injections of AO alone. We conclude that PLGA nanospheres are effective compounds for the sustained release of PEG-PEI-AO polyplexes in skeletal muscle and concomitant expression of dystrophin, and may have translational potential in treating DMD
The general classical solution of the superparticle
The theory of vectors and spinors in 9+1 dimensional spacetime is introduced
in a completely octonionic formalism based on an octonionic representation of
the Clifford algebra \Cl(9,1). The general solution of the classical
equations of motion of the CBS superparticle is given to all orders of the
Grassmann hierarchy. A spinor and a vector are combined into a
Grassmann, octonionic, Jordan matrix in order to construct a superspace
variable to describe the superparticle. The combined Lorentz and supersymmetry
transformations of the fermionic and bosonic variables are expressed in terms
of Jordan products.Comment: 11 pages, REVTe
Non-Riemannian Gravity and the Einstein-Proca System
We argue that all Einstein-Maxwell or Einstein-Proca solutions to general
relativity may be used to construct a large class of solutions (involving
torsion and non-metricity) to theories of non-Riemannian gravitation that have
been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and
Quantum Gravit
Black Holes with Weyl Charge and Non-Riemannian Waves
A simple modification to Einstein's theory of gravity in terms of a
non-Riemannian connection is examined. A new tensor-variational approach yields
field equations that possess a covariance similar to the gauge covariance of
electromagnetism. These equations are shown to possess solutions analogous to
those found in the Einstein-Maxwell system. In particular one finds
gravi-electric and gravi-magnetic charges contributing to a spherically
symmetric static Reissner-Nordstr\"om metric. Such Weyl ``charges'' provide a
source for the non-Riemannian torsion and metric gradient fields instead of the
electromagnetic field. The theory suggests that matter may be endowed with
gravitational charges that couple to gravity in a manner analogous to
electromagnetic couplings in an electromagnetic field. The nature of
gravitational coupling to spinor matter in this theory is also investigated and
a solution exhibiting a plane-symmetric gravitational metric wave coupled via
non-Riemannian waves to a propagating spinor field is presented.Comment: 18 pages Plain Tex (No Figures), Classical and Quantum Gravit
Octonionic representations of Clifford algebras and triality
The theory of representations of Clifford algebras is extended to employ the
division algebra of the octonions or Cayley numbers. In particular, questions
that arise from the non-associativity and non-commutativity of this division
algebra are answered. Octonionic representations for Clifford algebras lead to
a notion of octonionic spinors and are used to give octonionic representations
of the respective orthogonal groups. Finally, the triality automorphisms are
shown to exhibit a manifest \perm_3 \times SO(8) structure in this framework.Comment: 33 page
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