Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Srednicki — Quantum Field Theory · Problem 3.3
Canonical Quantization of Scalar Fields — Mark Srednicki
Physics — QFT · canonical-quantization-scalar-fields
Problem Use U ( Λ ) − 1 φ ( x ) U ( Λ ) = φ ( Λ − 1 x ) U(\Lambda)^{-1}\varphi(x)U(\Lambda) = \varphi(\Lambda^{-1}x) U ( Λ ) − 1 φ ( x ) U ( Λ ) = φ ( Λ − 1 x ) U ( Λ ) − 1 a ( k ) U ( Λ ) = a ( Λ − 1 k ) , U ( Λ ) − 1 a † ( k ) U ( Λ ) = a † ( Λ − 1 k ) , (3.34) \begin{aligned}
U(\Lambda)^{-1}a(\mathbf{k})U(\Lambda) &= a(\Lambda^{-1}\mathbf{k})\,, \notag\\
U(\Lambda)^{-1}a^\dagger(\mathbf{k})U(\Lambda) &= a^\dagger(\Lambda^{-1}\mathbf{k})\,, \tag{3.34}
\end{aligned} U ( Λ ) − 1 a ( k ) U ( Λ ) U ( Λ ) − 1 a † ( k ) U ( Λ ) = a ( Λ − 1 k ) , = a † ( Λ − 1 k ) , ( 3.34 ) U ( Λ ) ∣ k 1 … k n ⟩ = ∣ Λ k 1 … Λ k n ⟩ , (3.35) U(\Lambda)|k_1\ldots k_n\rangle = |\Lambda k_1\ldots\Lambda k_n\rangle\,, \tag{3.35} U ( Λ ) ∣ k 1 … k n ⟩ = ∣Λ k 1 … Λ k n ⟩ , ( 3.35 ) ∣ k 1 … k n ⟩ = a † ( k 1 ) … a † ( k n ) ∣ 0 ⟩ |k_1\ldots k_n\rangle = a^\dagger(\mathbf{k}_1)\ldots a^\dagger(\mathbf{k}_n)|0\rangle ∣ k 1 … k n ⟩ = a † ( k 1 ) … a † ( k n ) ∣0 ⟩ n n n k 1 , … , k n k_1,\ldots,k_n k 1 , … , k n Browse the problem library