Editing QuasiParticles (section)

=== Electron-Phonon Interaction ===
The interaction between electrons and phonons in a material is a key factor in determining electrical resistance and superconductivity. The Hamiltonian for this interaction is:

<math>H_{e-ph} = \sum_{k,q} g_q c_k^\dagger c_{k+q} (a_q + a_{-q}^\dagger)</math>

where:
* <math>H_{e-ph}</math> is the electron-phonon interaction Hamiltonian,
* <math>g_q</math> is the electron-phonon coupling constant,
* <math>c_k^\dagger</math> and <math>c_{k+q}</math> are the electron creation and annihilation operators,
* <math>a_q</math> and <math>a_{-q}^\dagger</math> are the phonon annihilation and creation operators.

This interaction is critical in the study of materials that exhibit superconductivity.

<sub>''Caption:'' These equations represent key mathematical concepts that describe the behavior and interactions of quasiparticles in condensed matter systems.''</sub>