Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
WolframQuantumComputation`DiracMatrix`
EuclideanGammaMatrices  |
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Details and Options
Examples
(6)
Basic Examples
(1)
The four Euclidean gamma matrices in dimension 4 (spinor dimension =4):
2
2
In[1]:=
 | EuclideanGammaMatrices |
Out[1]=
,
,
,
0 | 0 | 1 | 0 |
0 | 0 | 0 | -1 |
1 | 0 | 0 | 0 |
0 | -1 | 0 | 0 |
0 | 0 | - | 0 |
0 | 0 | 0 | |
| 0 | 0 | 0 |
0 | - | 0 | 0 |
0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 |
0 | - | 0 | 0 |
| 0 | 0 | 0 |
0 | 0 | 0 | - |
0 | 0 | | 0 |
Verify the Euclidean Clifford relation in dimension 4:
{,}=2I
μ
Γ
ν
Γ
μν
δ
In[2]:=
ModuleΓ=
[4],Outer[#1.#2+#2.#1&,Γ,Γ,1]2TensorProduct[IdentityMatrix[4],IdentityMatrix[4]]
 | EuclideanGammaMatrices |
Out[2]=
True
Scope
(2)
Applications
(1)
Possible Issues
(1)
Neat Examples
(1)
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