The geometry of coherent states

We examine the geometry of the state space of a relativistic quantum field. The mathematical tools used involve complex algebraic geometry and Hilbert space theory. We consider the Kähler geometry of the state space of any quantum field theory based on a linear classical field equation. The state space is viewed as an infinite-dimensional complex projective space. In the case of boson fields, a special role is played by the coherent states, the …