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Physics · L5 · Second Quantisation: From Particles to Fields

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Conceptual map of how quantum field theory promotes classical fields to operators and introduces creation/annihilation operators.

by @openstemUpdated Physics
Classical field φ(x,t)Promote to operator field φ̂(x,t)Expand in modes: â_k (annihilate), â†_k (create)Canonical (anti)commutation relations[â_k, â†_k'] = δ_{kk'}Fock space: |n_k₁, n_k₂, ...⟩Observables: number N̂ = Σ â†_k â_k, Hamiltonian ĤInteractions via coupling terms in Lagrangian density ℒ

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