ar X iv : h ep - t h / 01 10 07 9 v 2 1 5 N ov 2 00 1 Higher Derivative Gravity and Torsion from the Geometry of C - spaces
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چکیده
The geometry of curved Clifford space (C-space) is investigated. It is shown that the curvature in C-space contains higher orders of the curvature in the underlying ordinary space. A C-space is parametrized not only by 1-vector coordinates x µ but also by the 2-vector coordinates σ since they describe the holographic projections of 1-lines, 2-loops, 3-loops, etc., onto the coordinate planes. It is shown that when a scalar quantity or the components of a vector depend on the coordinates σ µν , then this indicates the presence of torsion.
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ar X iv : h ep - t h / 01 10 07 9 v 1 9 O ct 2 00 1 Higher Derivative Gravity and Torsion from the Geometry of C - spaces
The geometry of curved Clifford space (C-space) is investigated. It is shown that the curvature in C-space contains higher orders of the curvature in the underlying ordinary space. A C-space is parametrized not only by 1-vector coordinates x µ but also by the 2-vector coordinates σ since they describe the holographic projections of 1-lines, 2-loops, 3-loops, etc., onto the coordinate planes. It...
متن کاملar X iv : h ep - t h / 01 10 07 9 v 3 2 7 A pr 2 00 2 Higher Derivative Gravity and Torsion from the Geometry of C - spaces
We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension—the so called Clifford space (C-space), a manifold of points, lines, areas, etc..; physical quantities are Clifford algebra valued objects , called polyvectors. This provides a natural framework for description of super-symmetry, since spinors are just left or right ...
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تاریخ انتشار 2001