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Quantization of the Radiation Field
Physics — Quantum Mechanics · dirac-field-momentum-translation
Problem Prove that the momentum operator of the Dirac field (13.3.26)
P μ = ∑ k , r k μ [ b r k † b r k + d r k † d r k ] P^\mu = \sum_{\mathbf{k},r} k^\mu\left[b^\dagger_{r\mathbf{k}}b_{r\mathbf{k}} + d^\dagger_{r\mathbf{k}}d_{r\mathbf{k}}\right] P μ = k , r ∑ k μ [ b r k † b r k + d r k † d r k ] e i a μ P μ ψ ( x ) e − i a μ P μ = ψ ( x + a ) . \mathrm{e}^{\mathrm{i}a_\mu P^\mu}\psi(x)\mathrm{e}^{-\mathrm{i}a_\mu P^\mu} = \psi(x+a)\,. e i a μ P μ ψ ( x ) e − i a μ P μ = ψ ( x + a ) . Browse the problem library