Quantum field theory (QFT) is a theoretical framework that combines quantum mechanics and special relativity to describe the behavior of fundamental particles and their interactions. It is formulated in terms of harmonic oscillators due to several reasons:
Mathematical tractability: Harmonic oscillators have simple and well-understood mathematical properties. They can be described using mathematical techniques such as Fourier analysis and creation/annihilation operators, which facilitate calculations and allow for the development of consistent mathematical frameworks.
Quantization of fields: In quantum field theory, fields are treated as collections of harmonic oscillators. Each mode of the field corresponds to a separate harmonic oscillator. The quantization process involves promoting the field amplitudes to operators that satisfy commutation relations, leading to the creation and annihilation operators associated with harmonic oscillators.
Particle interpretation: In quantum field theory, particles are viewed as excitations of the underlying fields. Each particle corresponds to a specific mode of the field, and the number of particles in a mode is related to the occupation number of the corresponding harmonic oscillator. The quantization of the field allows for the creation and annihilation of particles through the corresponding creation and annihilation operators.
Energy quantization: Harmonic oscillators naturally exhibit discrete energy levels due to the quantization of their energies. This discrete energy spectrum aligns with the observed quantization of energy levels in quantum systems.
By formulating quantum field theory in terms of harmonic oscillators, physicists can describe the creation, annihilation, and interaction of particles consistently within the framework of quantum mechanics. It provides a powerful and elegant mathematical language to describe the behavior of quantum fields and their associated particles.