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Baker-Campbell-Hausdorff relation for special unitary groups SU(N)

Stefan Weigert
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Abstract

Multiplication of two elements of the special unitary group SU(N) determines uniquely a third group element. A BAker-Campbell-Hausdorff relation is derived which expresses the group parameters of the product (written as an exponential) in terms of the parameters of the exponential factors. This requires the eigen- values of three (N-by-N) matrices. Consequently, the relation can be stated analytically up to N=4, in principle. Similarity transformations encoding the time evolution of quantum mechanical observables, for example, can be worked out by the same means.

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Stefan Weigert. 1997-10-07. Baker-Campbell-Hausdorff relation for special unitary groups SU(N). https://doi.org/10.1088/0305-4470/30/24/032

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