Generalised coherent states and Bogoliubov transformations

Abstract

The authors study the properties of the states U2( rho , theta , lambda ) mod A) where U2 is an operator associated with the group SU(1,1), and mod A) is a standard (atomic or Glauber) coherent state defined in terms of the usual boson creation and destruction operators aDagger and a. They show how these states may be viewed as ordinary coherent states in terms of the Bogoliubov quasiparticles whose creation and destruction operators bDagger and b are associated with the operators aDagger and a by a Bogoliubov transformation. As an important example of the use of these states, they show that they are the coherent states associated with a uniformly accelerated (Rindler) observer moving through Minkowski space. The previous results then simply show how the Minkowski (inertial) vacuum appears to the Rindler observer as a black-body radiator with a Planckian distribution corresponding to a temperature proportional to the proper acceleration.