12 Questions
What are the entries of the SO(1,3) vector of four hermitian 2x2 matrices?
σ 0, σ x, σ y, σ z
What is the equation of motion for a massive 4-component spinor field Ψ(x) in the absence of interactions with external fields?
(iγ µ ∂µ - m) Ψ = 0
What algebra do the three σ i matrices obey?
SO(3) ≃ SU(2)
What are the Dirac matrices called?
Dirac matrices
What is the total number of gauge vector particles with massless and massive particles combined?
11
Which generators correspond to the electromagnetic charge operator?
T3, Y2
What does the electric charge of a field z depend on?
Both SUL(2) Cartan charge and hypercharge
In which representation do the SM elementary fermionic particles transform?
(3, 2, 1/3)
What is the field operator Aµ(x) responsible for in the relativistic covariant canonical quantization?
Creating and annihilating particle states
What is the role of the creation and annihilation operators a†λ(k) and aλ(k) in the quantization method?
Obeying canonical commutation relations
What does the T-product ⟨0|T {Aµ(x) Aµ(y)} |0⟩ represent in the quantization method?
Feynman-Green 2-point function Gµν(x, y)
How are particle states |k1,..,kn; λ1,..,λn⟩ obtained in this quantization method?
By acting on the vacuum state |0⟩ using monomials
Test your understanding of relativistic covariant canonical quantization and field operators in the context of SO(1, 3) Lorentz symmetry. Explore the mapping of classical wave functions to field operators and their role in creating and annihilating particle states.
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