Quantum field theory 3, Quantization of the field
Автор: OVR
Загружено: 2024-06-09
Просмотров: 215
Quantization is the process of converting a classical physical theory into a quantum one, transitioning from continuous classical variables to discrete quantum variables. In quantum mechanics, this involves promoting classical observables to operators on a Hilbert space and imposing commutation relations. Diagonalization, finding a basis where an operator like the Hamiltonian is diagonal, simplifies solving the system by reducing it to its eigenstates and eigenvalues. For instance, quantizing the Klein-Gordon field involves decomposing the field into Fourier components, promoting the field and its conjugate momentum to operators, and expressing the Hamiltonian in terms of creation and annihilation operators. This results in a Hamiltonian that resembles a collection of harmonic oscillators, with each mode corresponding to a quantum harmonic oscillator, thus linking quantization and diagonalization.
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