Clifform calculus with applications to classical field theories

Abstract

The authors present a concise introduction to Clifford algebraic techniques and calculus with Clifford-algebra-valued differential forms (which they call 'clifforms'). Some examples of applications demonstrate the efficiency of these methods. These comprise Dirac-Kahler operators, Lie group and Kaluza-Klein geometry, Gauss-Bonnet Lagrangians, their dimensional reduction, and on-minimal couplings of gravity and an Abelian gauge field generated in this way. Furthermore, they formulate the four-dimensional Einstein equations as a clifform equation and relate it to certain spinor equations.