When an element of SU(2) is written as a complex 2 × 2 matrix, it is simply a multiplication of column 2-vectors. It is known in physics as the spin-1/2 and, historically, as the multiplication of quaternions (more precisely, multiplication by a unit quaternion).

In mathematics, the special unitary group of degree n, denoted SU (n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication.

The Sukhoi Su-2 (Russian: Сухой Су-2) is a Soviet reconnaissance and light bomber aircraft used in the early stages of World War II. It was the first airplane designed by Pavel Sukhoi. The basic design received an engine and armament upgrade (Su-4) and was modified for the ground-attack role (ShB).

In standard Physics notation, the irreps of su2 (and hence SU(2)) are specified by the representation of the three spin matrices. It turns out that, up to unitary equivalence, there is exactly one unitary irreducible representation of dimension d, for d 1.

2025年3月5日 · The special unitary group SU_n(q) is the set of n×n unitary matrices with determinant +1 (having n^2-1 independent parameters). SU(2) is homeomorphic with the orthogonal group O_3^+(2). It is also called the unitary unimodular group and is a Lie group.

2017年4月25日 · For SU(2), no rotations about any other axis commute with L3, so the Cartan subalgebra is one dimensional. 67 We want to look for finite dimensional irreducible representations, and we have chosen to make Γ(L3) diagonal.

2.3 Left- and right- group translations on SU(2): Isometries of S3 We have shown that the group manifold for SU(2) is S3. In this section, we demonstrate that continuously generated coordinate transformations that are symmetries of the group manifold (“isometries”) encode invariance of the geometry under left- and right-group transformations.

2020年11月22日 · In mathematics, the special unitary group of degree n, denoted SU (n), is the group of n × n unitary matrices with determinant 1. The group operation is that of matrix multiplication.

SU(2). These Lie groups are not homeomorphic, as their fundamental groups are distinct. Also, by inspecting the adjoint action of a maximal torus, SU(2) has center f 1gof order 2 whereas SO(3) has trivial center (see HW7, Exercise 1(iii)), so they are not isomorphic as abstract groups.

The space Ri+Rj+Rk mapped onto SU(2) by the exponential function is the tangent space at 1 of SU(2), just as the line Ri is the tangent line at 1 of the circle SO(2). The three-dimensional space Ri+Rj+Rk is the tangent space of the 3-sphere S3 = SU(2) at the identity element.