Grassmann-Cartan algebra and Klein-Gordon equations (Q1059870)

Let \(V=(M,g)\) be a Riemannian space over an n-dimensional differentiable manifold M with a non-singular metric g. At each point we have a graded Grassmann-Cartan algebra \(\Lambda =\oplus^{n}_{p=0}\Lambda^ p\) of differential forms and the usual differential mappings d and \(\delta\). The author studies the equations \((d+\delta +m)\alpha =0\), \(\alpha\in \Lambda\), and thus independently arrives at the so-called Dirac-Kähler equations, since there is no reference to many papers under this name. Then he reviews carefully and in detail the general geometrical notions, the properties of the above equation, special cases and some special explicit solutions.