Special orthogonal algebra

The algebra (2.3) is called the special orthogonal algebra in three dimensions, SO(3). Associated with each Lie algebra there is a group of transformation... 

S0(3) Group Algebra. The collection of matrices in Euclidean 3D space which are orthogonal and moreover for which the determinant is +1 is a subgroup of 0(3). SO(3) is the special orthogonal group in three variables and defines rotations in 3D space. Rotation of the Riemann sphere is a rotation in tM2... 

In the following, we pay special attention to the connections among the spherical, Stark and Zeeman basis. Since in momentum space the orbitals are simply related to hyperspherical harmonics, these connections are given by orthogonal matrix elements similar (when not identical) to the elements of angular momentum algebra. 

The extension of vector-algebraic techniques to multicomponent systems of higher dimensionality (degrees of freedom /> 2) can be carried out straightforwardly, even though one loses the convenience of mutually complementary pairs (X, X ) and orthogonal complementary conjugates (X, x ) that are a special feature of /= 2. In a space of / dimensions, a... 

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