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

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 $3 \times 3$ 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

Identification of prognostic factors and risk groups in patients found to have nodal metastasis at the time of radical hysterectomy for early-stage squamous carcinoma of the cervix

In a retrospective study conducted at the University of Alabama at Birmingham, the University of Michigan, and the Mayo Clinic, 185 patients with previously untreated FIGO stage IB and IIA squamous cell carcinoma of the cervix were found to have nodal metastasis at the time of radical hysterectomy and pelvic lymphadenectomy. Of these patients, 103 received adjuvant pelvic irradiation. Cancer recurred in 76 patients; the median time to recurrence was 3.1 years. The prognostic significance of patient age, clinical stage, lesion diameter, number and location of nodal metastases, and use of adjuvant radiation therapy was determined by multivariate analysis. Only patient age (P = 0.0006), lesion diameter (P P = 0.0004) were noted to be significant factors in determining overall survival. Rates of recurrence were also related to these factors. Employment of these significant variables led to identification of four risk groups. In general, patients with small cervical lesions (diameter 4 cm) and more than two involved nodes fell into the high-risk category. All other patients were categorized into intermediate-risk groups. Ten-year survival was 92% in the low-risk group (n = 13), 70% in the low-intermediate-risk group (n = 66), 56% in the high-intermediate-risk group (n = 66), and 13% in the high-risk group (n = 20). This risk group classification identifies subgroups of early-stage cervical carcinoma patients found to have nodal metastasis at the time of radical hysterectomy that warrant appropriately selected adjuvant therapy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27695/1/0000081.pd

Ferrotoroidic ground state in a heterometallic {Cr^IIIDy^III<inf>6</inf>} complex displaying slow magnetic relaxation

© 2017 The Author(s). Toroidal quantum states are most promising for building quantum computing and information storage devices, as they are insensitive to homogeneous magnetic fields, but interact with charge and spin currents, allowing this moment to be manipulated purely by electrical means. Coupling molecular toroids into larger toroidal moments via ferrotoroidic interactions can be pivotal not only to enhance ground state toroidicity, but also to develop materials displaying ferrotoroidic ordered phases, which sustain linear magneto-electric coupling and multiferroic behavior. However, engineering ferrotoroidic coupling is known to be a challenging task. Here we have isolated a {CrIIIDyIII6} complex that exhibits the much sought-after ferrotoroidic ground state with an enhanced toroidal moment, solely arising from intramolecular dipolar interactions. Moreover, a theoretical analysis of the observed sub-Kelvin zero-field hysteretic spin dynamics of {CrIIIDyIII6} reveals the pivotal role played by ferrotoroidic states in slowing down the magnetic relaxation, in spite of large calculated single-ion quantum tunneling rates