quantum mechanics - Why is there this relationship between
These matrices are traceless, Hermitian (so they can generate unitary matrix group elements through exponentiation), and obey the extra trace orthonormality relation. These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU (2) to SU (3), which formed the basis for Gell-Mann's quark model. Special linear group - Wikipedia In mathematics, the special linear group SL(n, F) of degree n over a field F is the set of n × n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion.This is the normal subgroup of the general linear group given by the kernel of the determinant: (,) → ×. where we write F × for the multiplicative group of F (that is, F excluding 0). The Vector Space Consisting of All Traceless Diagonal May 23, 2017 Dimension of Lie groups - McGill Physics
Since the latter matrices can be uniquely expressed as the exponential of symmetric traceless matrices, then this latter topology is that of (n + 2)(n − 1)/2-dimensional Euclidean space. Thus, the group SL(n, R) has the same fundamental group as SO(n), that is, Z for n = 2 and Z 2 for n > 2. Relations to other subgroups of GL(n,A)
Jan 25, 2003 Traceless tensors and the symmetric group - ScienceDirect Nov 01, 1979 Hyperfine Interaction – Electron Paramagnetic Resonance
Jul 05, 2018
We analyze the semi-classical and quantum behavior of the Bianchi IX Universe in the Polymer Quantum Mechanics framework, applied to the isotropic Misner variable, linked to the space volume of the model. The study is performed both in the Hamiltonian and field equations approaches, leading to the remarkable result of a still singular and chaotic cosmology, whose Poincaré return map