Electromagnetism in the Algebra of Physical Space

An increasing number of researchers advocate Geometric Algebra as the optimal language for unifying and simplifying physics. In this presentation, I will demonstrate this potential virtue of geometric algebra the context of electromagnetism by re-expressing all of Maxwell's equations as one single equation, which is not possible in the traditional formalisms of vector calculus and differential forms. This isolated equation completes the simplifying process initiated by the advent of vector calculus, which captures all of Maxwell's eight scalar equations in a neat set of four vector equations, providing insight into their geometric structure of the fields through notions such as divergence and curl. The expression of Maxwell's equations is further refined through the use of differential forms, which allow Maxwell's four vector equations to be expressed as two equations of differential forms. In this talk, I will show that the language of geometric algebra has sufficient power to express all of Maxwell's equations into one single multivector equation with computational and pedagogical advantages.