Abstract
A theory based on the concept of 16-dimensional Clifford space \(\mathcal C\), a manifold whose tangent space is Clifford algebra, is investigated. The elements of the space \(\mathcal C\) are oriented r-volumes, r = 0, 1, 2, 3, associated with extended objects such as strings and branes. Although the latter objects form an infinite dimensional configuration space, they can be sampled in terms of a finite dimensional subspace, namely, the Clifford space. The connection and the curvature of \(\mathcal C\) describe what, from the point of view of 4-dimensional spacetime, appear as gravitation and Yang-Mills gauge fields and field strengths. This is demonstrated on the case of a Clifford algebra valued field Ψ(X) which depends on position X in \(\mathcal C\) and satisfies the generalized Dirac equation.
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