Application of the double numbers in the representation of the Lorentz transformations




Lorentz transformations, double numbers, Wigner angle, Thomas precession


We show that the orthochronous proper Lorentz transformations that leave one of the Cartesian coordinates fixed can be represented by $2 \times 2$ unitary matrices with determinant equal to 1, whose entries are double numbers. This representation is employed in the calculation of the Wigner angle, which arises in the composition of two boosts in arbitrary directions.


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How to Cite

G. F. Torres del Castillo, “Application of the double numbers in the representation of the Lorentz transformations”, Rev. Mex. Fis. E, vol. 20, no. 1 Jan-Jun, pp. 010204 1–, Jan. 2023.