Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Srednicki — Quantum Field Theory · Problem 39.2
Canonical Quantization of Scalar Fields — Mark Srednicki
Physics — QFT · canonical-quantization-spinor-fields-ii
Problem Use [ Ψ ( x ) , M μ ν ] = − i ( x μ ∂ ν − x ν ∂ μ ) Ψ ( x ) + S μ ν Ψ ( x ) [\Psi(x), M^{\mu\nu}] = -i(x^\mu\partial^\nu - x^\nu\partial^\mu)\Psi(x) + S^{\mu\nu}\Psi(x) [ Ψ ( x ) , M μν ] = − i ( x μ ∂ ν − x ν ∂ μ ) Ψ ( x ) + S μν Ψ ( x ) J z b s † ( p z ^ ) ∣ 0 ⟩ = 1 2 s b s † ( p z ^ ) ∣ 0 ⟩ , J_z\, b_s^\dagger(p\hat{\mathbf{z}})|0\rangle = \tfrac{1}{2}s\, b_s^\dagger(p\hat{\mathbf{z}})|0\rangle\,, J z b s † ( p z ^ ) ∣0 ⟩ = 2 1 s b s † ( p z ^ ) ∣0 ⟩ , J z d s † ( p z ^ ) ∣ 0 ⟩ = 1 2 s d s † ( p z ^ ) ∣ 0 ⟩ , (39.38) J_z\, d_s^\dagger(p\hat{\mathbf{z}})|0\rangle = \tfrac{1}{2}s\, d_s^\dagger(p\hat{\mathbf{z}})|0\rangle\,, \tag{39.38} J z d s † ( p z ^ ) ∣0 ⟩ = 2 1 s d s † ( p z ^ ) ∣0 ⟩ , ( 39.38 ) p = p z ^ \mathbf{p} = p\hat{\mathbf{z}} p = p z ^ z ^ \hat{\mathbf{z}} z ^ z z z Browse the problem library