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Corinne A. Manogue

Publications and source records attributed to Corinne A. Manogue.

24 records · Page 2Linked to original sources
arXiv1998

Dimensional Reduction

Using an octonionic formalism, we introduce a new mechanism for reducing 10 spacetime dimensions to 4 without compactification. Applying this mechanism to the free, 10-dimensional, massless (momentum space) Dirac equation results in a particle spectrum consisting of exactly 3 generations. Each generation contains 1 massive spin-1/2 particle with 2 spin states, 1 massless spin-1/2 particle with only 1 helicity state, and their antiparticles --- precisely one generation of leptons. There is also a single massless spin-1/2 particle/antiparticle pair with the opposite helicity and no generation structure. We conclude with a discussion of some further consequences of this approach, including those which could arise when using the formalism on a curved spacetime background, as well as the implications for the nature of spacetime itself.

hep-th↗
arXiv1996

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.

gr-qc↗
arXiv1994

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.

hep-th↗
arXiv1993

The Scalar Field Equation in the Presence of Signature Change

We consider the (massless) scalar field on a 2-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal) size of the spacelike regions and not on the detailed form of the metric. Reformulating the problem using junction conditions, we then show that the solutions obtained above are the unique ones which satisfy the natural distributional wave equation everywhere. We also give a variational approach, obtaining the same results from a natural Lagrangian. (PACS numbers 04.20.Cv and 02.40.+m.)

gr-qc↗
arXiv1993

Finite Lorentz Transformations, Automorphisms, and Division Algebras

We give an explicit algebraic description of finite Lorentz transformations of vectors in 10-dimensional Minkowski space by means of a parameterization in terms of the octonions. The possible utility of these results for superstring theory is mentioned. Along the way we describe automorphisms of the two highest dimensional normed division algebras, namely the quaternions and the octonions, in terms of conjugation maps. We use similar techniques to define $SO(3)$ and $SO(7)$ via conjugation, $SO(4)$ via symmetric multiplication, and $SO(8)$ via both symmetric multiplication and one-sided multiplication. The non-commutativity and non-associativity of these division algebras plays a crucial role in our constructions.

hep-th↗