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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.
In the study of the representation theory of Lie groups, the study of representations of SU (2) is fundamental to the study of representations of semisimple Lie groups. It is the first case of a Lie group that is both a compact group and a non-abelian group.
• 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.
8 Ιουλ 2024 · 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.
22 Νοε 2020 · 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).
25 Απρ 2017 · However, we know that e4πiL3 = 1I, so e4πim = 1, and m = n/2 for some integer n, for us to have a true representation of the SU(2) group. But even without assuming this, we will find it anyway, from requiring the representation to be finite dimensional. From L1 and L2 we can form the two operators.
Group Definition. SU(2) is the group of all 2 x 2 unitary matrices with determinant 1, elements are Complex. SU(3) is the group of all 3 x 3 unitary matrices with determinant 1, elements are Complex. Unitary matrix U, U†U=I. SO(3) is the group of all 3 x 3 orthogonal matrices with determinant 1, elements are Real.
