Dual space and Clifford algebras (Q1895830)

The importance of the statement whether a quantity belongs to the base space or to its dual (for example in mechanics whether we have a velocity like vector or a wave-vector like covector) is discussed. The use of Clifford algebras in the study of spaces, like space-time in physics, is analyzed. Vectors and covectors can be treated, because of the assumed existence of a Riemannian metric, without an explicit reference of their base space or dual space nature. The concept of configuration space and reciprocal space in solid state physics and the case of \(X\)-ray crystallography are mentioned. The relation of vectors, covectors, multivectors and multicovectors is analyzed.