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A commutative algebra, function theory, and system of analysis is developed for one 4-D variable (not quaternions). It is based upon a commutative group ring and extends all of the properties of the classical complex variables.
A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.
Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations.
A simple review of the powerful technique of dimensional analysis.
A brief introduction to the properties and uses of the Dirac delta function. [PDF]
A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.
A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
Lecture notes from the ITP miniprogram on Geometry and Duality
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