) so you could easily construct them in - for example - the adjoint representation. The SU(8) group, also known as the Special Unitary Group of degree 8, is a mathematical group that consists of all 8x8 unitary matrices with determinant 1. It is a type of Lie group, which is a group that is also a smooth manifold.
The generators of the SU(8) group are 63 complex matrices that are used to generate all other matrices in the group through linear combinations. These generators are often represented as the Gell-Mann matrices, which are a set of matrices commonly used in the study of SU(N) groups.
The generators of the SU(8) group form a basis for the Lie algebra, which is a vector space that captures the algebraic structure of the group. The Lie algebra associated with the SU(8) group is known as su(8) and has a dimension of 63.
The SU(8) group has applications in various fields such as particle physics, quantum mechanics, and string theory. It is used to describe the symmetries of certain physical systems and to study the behavior of particles and their interactions.
Yes, the SU(8) group is an important tool in the study of symmetry breaking, which is the phenomenon where a system exhibits a lower level of symmetry than its underlying laws. This group is particularly relevant in the study of grand unified theories, which attempt to unify all fundamental interactions in physics.