I have recently learned about the Unruh effect and the fact that when going from a stationary to an accelerated reference frame the quantum state is updated by a Bogoliubov transformation.

Does every Bogoliubov transformation correspond to a new motion/orientation of an observer in spacetime? If so what is this set of motions/orientations?


The answer is no, not every Bogoliubov transformation corresponds to a new motion/orientation of an observer.

Usually, Bogoliubov transformations are used in quantum statistical physics, where the system is at equilibrium, and there is no time appearing. In that case, they amount to define new operators such that the new annihilation operator annihilates the (interacting) ground-state of the system.

  • $\begingroup$ If I put a quantum field on a spacetime and boost to an accelerating reference frame then the field modes undergo squeezing which is a Bogoliubov transformation (or, as I come from quantum optics, a symplectic transformation). Is it the case that no other transformations on spacetime have a Bogoliubov effect on the fields, for example Lorentz boosts? Are accelerations unique in this sense? $\endgroup$ – Matta Oct 6 '16 at 7:43

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