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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.
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.
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.
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.
22 Νοε 2020 · 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.
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.
The group SU(2) is the group of unitary 2 2 complex matrices with determinant 1. Every such matrix can be uniquely written as. U(z;w) = z w ! w z. for (z;w) 2 C2, with the condition that jzj2 + jwj2 = 1. In other words, SU(2) is topologically equivalent to the unit sphere in C2, which is the same as the real 3-sphere.
