Gell-Mann matrices
E33749
Gell-Mann matrices are a set of eight 3×3 traceless Hermitian matrices that serve as the generators of the SU(3) Lie algebra in quantum chromodynamics and other areas of particle physics.
Aliases (1)
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
Lie algebra generators
→
SU(3) generators → mathematical object → matrix basis set → |
| actOn |
color triplet of quarks
→
flavor triplet of quarks → three-component complex vectors → |
| are |
Hermitian
→
linearly independent → traceless → |
| basisOf |
space of traceless Hermitian 3×3 matrices
→
|
| belongTo |
fundamental representation of SU(3)
→
|
| cardinality |
8
→
|
| componentType |
complex entries
→
|
| dimension |
3×3
→
|
| field |
particle physics
→
quantum chromodynamics → theoretical physics → |
| generalizationOf |
Pauli matrices to SU(3)
→
|
| generate |
SU(3) Lie algebra
→
|
| haveProperty |
off-diagonal elements for λ1, λ2, λ4, λ5, λ6, λ7
→
real diagonal elements for λ3 and λ8 → |
| indexRange |
a = 1,…,8
→
|
| matrixSize |
3 by 3
→
|
| namedAfter |
Murray Gell-Mann
→
|
| normalization |
Tr(λ_a λ_b) = 2 δ_{ab}
→
|
| numberOfElements |
8
→
|
| relatedTo |
Pauli matrices
→
|
| satisfy |
[λ_a, λ_b] = 2 i f_{abc} λ_c
→
su(3) commutation relations → {λ_a, λ_b} = 4/3 δ_{ab} I + 2 d_{abc} λ_c → |
| span |
Lie algebra su(3)
→
|
| symbol |
λ_a
→
|
| usedFor |
classifying hadrons in the Eightfold Way
→
constructing SU(3) group elements via exponentiation → defining QCD gauge fields → writing QCD covariant derivative → |
| usedIn |
SU(3) Lie algebra
→
color SU(3) symmetry → flavor SU(3) symmetry → gauge theories → quantum field theory → quark model → representation theory → |
| usedToRepresent |
color charge operators
→
flavor symmetry generators → |
Referenced by (2)
| Subject (surface form when different) | Predicate |
|---|---|
|
Murray Gell-Mann
→
|
knownFor |
|
Gell-Mann matrices
("[λ_a, λ_b] = 2 i f_{abc} λ_c")
→
|
satisfy |