What is the fundamental representation of SU 2?

What is the fundamental representation of SU 2?

SU(2) symmetry also supports concepts of isobaric spin and weak isospin, collectively known as isospin. in the physics convention) is the 2 representation, the fundamental representation of SU(2). When an element of SU(2) is written as a complex 2 × 2 matrix, it is simply a multiplication of column 2-vectors.

What is an SU 2 transformation?

SU(2) corresponds to special unitary transformations on complex 2D vectors. The natural representation is that of 2×2 matrices acting on 2D vectors – nevertheless there are other representations, in particular in higher dimensions.

Is Su 2 a simple group?

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 Zn.

What is SU2 and SU3?

It gave the definition of SU2 as the group of unitary 2*2 matrices and that SU3 is the group of unitary 3*3 matrices.

How many independent generators would the group SU N have?

Matrix 3 × 3 has nine complex numbers (in general for SU(n) it has n2 complex parameters) and there are 8 generator (for SU(n) we have n2 − 1) plus unit matrix, which gives also 9 terms (n2), i.e. again 9 complex parameters.

What is Su matrix?

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 more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication.

What does SU 3 represent?

SU(3) is called the adjoint representation of SU(3). The SU(3) generators or charges Ta, a = 1, . . . , 8, form an eight-dimensional adjoint representation of SU(3). In general, every SU(3) representation exhibits threefold symmetry in the (T3, T8) plane.

Is Su n Simply Connected?

SU(n) is simply connected. S2n+1 Since n ≥ 1 and π1(S2n+1) = π2(S2n+1) = 0, we get the following LES: …

Is Su n Compact?

Properties. The special unitary group SU(n) is a real Lie group (though not a complex Lie group). Its dimension as a real manifold is n2 − 1. Topologically, it is compact and simply connected.

What is the dimension of so N?

Group structure The groups O(n) and SO(n) are real compact Lie groups of dimension n(n − 1)/2. The group O(n) has two connected components, with SO(n) being the identity component, that is, the connected component containing the identity matrix.

How many generators do so 3 and SU 3 have?

Why $SU(3)$ has eight generators? – Physics Stack Exchange.