### Corinne A. Manogue

**THEORETICAL PHYSICS RESEARCH--OVERVIEW**

**Dimensional Reduction and Octonions **

My long-term goal in this research is to describe the fundamental symmetries
of physics by exploiting the symmetries inherent in exceptional mathematical
structures involving the octonions, a non-commutative, non-associative
extension of the complex numbers.

My results have included:

a demonstration that the non-linear Virasoro constraints of bosonic
string theory and the superstring equations in 10-dimensions are both simple
restatements of the octonionic multiplication rule;
an explicit alternative to exponentiation for the description of finite
Lorentz transformations which evades the twin hazards of non-commutativity
and non-associativity;
an exploration of the eigenvectors and eigenvalues of octonionic matrices;
a generalization of Mobius transformations to ten-dimensions, laying the groundwork
for a possible relationship between twistor theory and superstring theory;
a proposal to use the octonionic formalism to reduce ten spacetime
dimensions to four, without the usual compactification required by superstring
theory;
the application of this symmetry breaking to the Dirac equation resulting
in a particle spectrum with the correct number of generations and spin/helicity
properties to describe precisely three generations of leptons.
**Field Theory in Curved Spacetime **

What different physical phenomena can create particles out of the vacuum? Beginning
with Klein's suggestion (soon after the Dirac equation was postulated) that
strong electric fields should spontaneously create particles, and revivified
with Hawking's proposal that black holes should also do so, this question has
always been central to the interpretation of quantum field theory in background
spacetimes. Surprisingly, the key is usually a precise, unambiguous definition
of the vacuum itself.

My own contributions have included:

- correcting a physically crucial sign error in the standard textbook treatment
of the Klein paradox to show that bosons can be superradiant, but not fermions;
- generalizing ``Casimir Effect'' calculations to rotating boundaries to show
that it is possible to “stir” the vacuum;
- discovering that rotating particle detectors will not detect particles if
the vacuum can be defined unambiguously;
- showing that, even for the most general possible physical propagation rule,
changes of topology at a single point cause infinite production of energy
and (bosonic) particles;
- finding the most general possible boundary conditions that conserve current
in signature changing spacetimes.

While these research problems involve deep issues regarding the interpretation
of quantum field theory, the calculations themselves involve simple models,
carefully chosen to illuminate the important physics while minimizing mathematical
complications. Research on these problems is certainly accessible to graduate
students and often to undergraduates.

*Much of the work discussed here has been completed in collaboration with
other scientists. Please see my publication list for
details. *

If you have comments or suggestions, email me at *corinne@physics.oregonstate.edu*

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*Last Update 6/17/09*

© *Corinne Manogue, 2005.*