A O Barut et al 1994 J. Phys. A: Math. Gen. 27 5239 doi:10.1088/0305-4470/27/15/022
A O Barut, J R Zeni and A Laufer
Show affiliationsWe present a general method to obtain a closed finite formula for the exponential map from the Lie algebra to the Lie group for the defining representation of orthogonal groups. Our method is based on the Hamilton-Cayley theorem and some special properties of the generators of the orthogonal group and is also independent of the metric. We present an explicit formula for the exponential of generators of the SO+(p,q) groups with p+q=6, in particular, dealing with the conformal group SO+(2,4) which is homomorphic to the SU(2,2) group. This result is needed in the generalization of U(1)-gauge transformations to spin-gauge transformations where the exponential plays an essential role. We also present some new expressions for the coefficients of the secular equation of a matrix.
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
Issue 15 (7 August 1994)
A O Barut et al 1994 J. Phys. A: Math. Gen. 27 5239
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