Representations of SU(2) describe non-relativistic spin, due to being a double covering of the rotation group of Euclidean 3-space. Relativistic spin is described by the representation theory of SL 2 (C), a supergroup of SU(2), which in a similar way covers SO + …

The SU(n) groups find wide application in the Standard Model of particle physics, especially SU(2) in the electroweak interaction and SU(3) in quantum chromodynamics. [1] The simplest case, SU(1), is the trivial group, having only a single element. The group SU(2) is isomorphic to the group of quaternions of norm 1, and is thus diffeomorphic to ...

2020年12月25日 · su(2)群是所有行列式为1的二阶幺正矩阵构成的群，s表示行列式为1，u表示幺正，2表示二阶。 任意二阶幺正矩阵可以表示为 \left[ \begin{array}{c c} a&b\\ -b^* &a^* \end{array} \right] ，令a=x1+ix2, b=x3+ix4，那么行列式为1等价于 x_1^2+x_2^2+x_3^2+x_4^2 = 1 ，即四维空间中的一个球面。

The groupSU(2) is the group of unitary 22 complex matrices with determinant 1. Every such matrix can be uniquely written as U(z;w) = z w w z! for(z;w) 2C2, with the condition thatjzj2 +jwj2 = 1. In other words,SU(2) is topologically equivalent to the unit sphere in C2, which is the same as thereal 3-sphere. SU(2) is a real Lie

• SU(2) describes spin angular momentum. • SU(2) is isomorphic to the description of angular momentum – SO(3). • SU(2) also describes isospin – for nucleons, light quarks and the weak interaction. • We see how to describe hadrons in terms of several quark wavefunctions.

2020年11月22日 · The special unitary group SU(n) is a real matrix Lie group of dimension n 2 − 1. Topologically, it is compact and simply connected. Algebraically, it is a simple Lie group (meaning its Lie algebra is simple; see below). The center of SU(n) is isomorphic to the cyclic group Z n.

2016年8月5日 · The group $SO(2)$ is defined to be the group of $2 \times 2$ real orthogonal matrices (the vector space being $\mathbb{R}^2$ over $\mathbb{R}$). The group $SU(2)$ is defined to be the group of $2 \times 2$ complex unitary matrices (the vector space being $\mathbb{C}^2$ over $\mathbb{C}$). $\endgroup$

2016年7月22日 · The $SU(2)$ triplet results from the Adjoint Representation $\mathrm{Ad}: SU(2)\to SO(3)$ of $SU(2)$, whereby $SU(2)$ acts on its own Lie algebra. As a $2\times2$ matrix, an element of the Lie algebra $\mathfrak{su}(2)$ can be written:

2019年6月28日 · The SU (2) Lie algebra su (2) forms a 3-dimensional real vector space and is therefore an Abelian group under addition. Like any group ( su ( 2 ), +) satisfies the following conditions:

In particle physics, SU(1), SU(2), and SU(3) are special unitary groups that play a fundamental role in describing the symmetries of elementary particles and their interactions. These groups are associated with different types of quantum fields and have important implications in the theory of quantum chromodynamics (QCD) and the electroweak theory.