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Representation of the Lorentz transformations in 6-dimensional space-time. (English) Zbl 1265.83003

Summary: We consider first the space-time as a principal bundle with structure group \(SO(3,\mathbb C)\) over the base \(B=\mathbb R^3\). From this viewpoint the 4-vector of velocity is replaced now by a \(3\times 3\) orthogonal Hermitian matrix. Starting from the structure group \(SO(3,\mathbb C)\) the Lorentz transformations are written in 6 dimensions. Further it is considered a more sophisticated model of space-time with the same structural group \(SO(3,\mathbb C)\) over the base \(SO(3,\mathbb R)\). In this model there are only rotations, but no translations. So the Lorentz transformations are also converted for this bundle.

MSC:

83A05 Special relativity
83F05 Relativistic cosmology
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