Bogoliubov transformation

Summary

A Bogoliubov transformation is a linear change of creation and annihilation operators that mixes creation with annihilation operators and keeps their commutation or anticommutation relations. It gives a new set of modes, and so a new notion of particle and of vacuum. It is the standard tool to diagonalize quadratic Hamiltonians, as in the theory of superfluidity and superconductivity. In quantum field theory in curved spacetime it relates the particle notions of different observers and gives particle creation and the Unruh effect.