Pauli matrices #
The tensor σ^μ^a^{dot a}
based on the Pauli-matrices as an element of
complexContr ⊗ leftHanded ⊗ rightHanded
.
Equations
- PauliMatrix.asTensor = ∑ i : Fin 1 ⊕ Fin 3, Lorentz.complexContrBasis i ⊗ₜ[ℂ] Fermion.leftRightToMatrix.symm ↑(PauliMatrix.σSA i)
Instances For
The expansion of asTensor
into complexContrBasis basis vectors .
The expansion of the pauli matrix σ₀
in terms of a basis of tensor product vectors.
The expansion of the pauli matrix σ₁
in terms of a basis of tensor product vectors.
The expansion of the pauli matrix σ₂
in terms of a basis of tensor product vectors.
The expansion of the pauli matrix σ₃
in terms of a basis of tensor product vectors.
The expansion of asTensor
into complexContrBasis basis of tensor product vectors.
The tensor σ^μ^a^{dot a}
based on the Pauli-matrices as a morphism,
𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ leftHanded ⊗ rightHanded
manifesting
the invariance under the SL(2,ℂ)
action.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The map 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ leftHanded ⊗ rightHanded
corresponding
to Pauli matrices, when evaluated on 1
corresponds to the tensor PauliMatrix.asTensor
.