Octonions, E6, and Particle Physics

In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be described by Hermitian matrices over the complexes or quaternions. The remaining, exceptional Jordan algebra can be described by 3x3 Hermitian matrices over the octonions. We first review properties of the octonions and the exceptional Jordan algebra, including our previous work on the octonionic Jordan eigenvalue problem. We then examine a particular real, noncompact form of the Lie group E6, which preserves determinants in the exceptional Jordan algebra. Finally, we describe a possible symmetry-breaking scenario within E6: first choose one of the octonionic directions to be special, then choose one of the 2x2 submatrices inside the 3x3 matrices to be special. Making only these two choices, we are able to describe many properties of leptons in a natural way. We further speculate on the ways in which quarks might be similarly encoded.Comment: 13 pages; 6 figures; TonyFest plenary talk (York 2008

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

Small Kerr-anti-de Sitter black holes are unstable

Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.Comment: 7 pages, 1 figure, RevTeX

Gravity and Signature Change

The use of proper ``time'' to describe classical ``spacetimes'' which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.Comment: Plain TeX, 6 pages; to appear in GR

The Rotating Quantum Vacuum

We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to their motion. Applications involving possible violations of the second law of thermodynamics are briefly addressed.Comment: Plain TeX, 10 pages (to appear in PRD

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

Detecting the rotating quantum vacuum

We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to their motion. Applications involving possible violations of the second law of thermodynamics are briefly addressed

Capturing differences in dental training using a virtual reality simulator

Virtual reality simulators are becoming increasingly popular in dental schools across the world. But to what extent do these systems reflect actual dental ability? Addressing this question of construct validity is a fundamental step that is necessary before these systems can be fully integrated into a dental school's curriculum. In this study, we examined the sensitivity of the Simodont (a haptic virtual reality dental simulator) to differences in dental training experience. Two hundred and eighty-nine participants, with 1 (n = 92), 3 (n = 79), 4 (n = 57) and 5 (n = 61) years of dental training, performed a series of tasks upon their first exposure to the simulator. We found statistically significant differences between novice (Year 1) and experienced dental trainees (operationalised as 3 or more years of training), but no differences between performance of experienced trainees with varying levels of experience. This work represents a crucial first step in understanding the value of haptic virtual reality simulators in dental education

Distributional Modes for Scalar Field Quantization

We propose a mode-sum formalism for the quantization of the scalar field based on distributional modes, which are naturally associated with a slight modification of the standard plane-wave modes. We show that this formalism leads to the standard Rindler temperature result, and that these modes can be canonically defined on any Cauchy surface.Comment: 15 pages, RevTe

Should prospective dental students be screened for colour vision deficits?

A perennial question in dental education is: what skills and aptitudes should be assessed in prospective dental students? Intellectual capacity and manual dexterity understandably rank highly, but are there minimum thresholds for visual perception that applicants need be able to demonstrate before they enter the profession? We have recently flagged this issue with regard to the thresholds of stereoscopic acuity required for a dentist when operating on teeth. In the present article, we highlight the issue of identifying a minimum acceptable level of colour vision