(i)

Clifford Algebras

- Published a construction and classification of Clifford algebras, and defined their finite groups (sometimes referred to as the Salingaros groups)

- Unified many of the algebraic structures that arise in physical descriptions into one setting, by using a differential form basis for the Clifford Algebras

- Evaluated the exponential mapping in the three-dimensional Clifford algebras, presenting a general analytic form of the Campbell-Baker-Hausdorff formula (with J. Froelich)

- Clarified the relationship between twistors and Clifford algebras (with R. Ablamowicz)
(ii)

Electromagnetic Field Theory

- Gave closed-form analytic formulas for generalized trace identities in quantum electrodynamics (with M. Dresden)

- Showed that electromagnetic fields are the holomorphic fields of Minkowski spacetime, which appears only in the differential-form realization of the spacetime Clifford Algebra

- Computed trajectories of charged particles in magnetic fields. This result checks and corrects previously published results by other authors, and gives a general expression for the relativistic gyrofrequency

- Described the Thomas precession of spinning charges in a general setting

- Derived higher-order invariants of the electromagnetic field under Lorentz transformations and Duality rotations

- Gave a general prescription for the construction of field theories by identifying algebraic idempotents with physical observables (with G. P. Wene). This identifies the spin degree of freedom as a fifth physical dimension
(iii)

Plasma Physics and Thermonuclear Fusion

- Introduced the
Fiber Theory of Plasmasas a general and practical theoretical description of plasma currents- Provided a unified model of diffuse plasma pinches in all cylindrically-symmetric geometries
- Derived a theoretical value for the Reversed-Field Pinch parameter at criticality as Theta
_{0}= 1.41, which is more accurate than that obtained from the Bessel-function model- Contributed to the understanding of "force-free configurations", and resolved the paradox of electromagnetic waves with
Eparallel toB- This work identifies an intrinsic instability observed in the Spheromak machine, which was overlooked because of an original miscomputation of the magnetic fields
- Applied the
fiber theoryto describe oscillations and reconnections in Tokamak machines (with R. Carrera)- Described the stability, evolution, and disruption of the frozen deuterium Z-pinch
- Proposed a fusion reactor with a spherical configuration, and established its advantages over one with a toroidal geometry (with E. Panarella)
(iv)

Superconducting Magnets and Magnetohydrodynamic Generators

- Made contributions to the theory of force-reduced electromagnet windings
- Designed an optimized cable for superconducting energy storage
- Proposed this design as a significant large-scale mechanism for magnetic energy storage in space plasmas
- Gave a classification of cylindrically-symmetric magnetohydrodynamic generators. One of these provides a model for magnetic elements in the solar photosphere (with P. Lorrain)