I am looking for a qualitative explanation, if possible, of the following passage from Peskin & Schroeder, bottom of page 26, concerning the quantised real Klein-Gordon field:
A positive frequency solution of the field equation has as its coefficient the operator that destroys a particle in that single particle wavefunction. A negative frequency solution of the field equation, being the Hermitian conjugate of a positive frequency solution, has as its coefficient the operator that creates a particle in that positive energy single particle wavefunction. In this way, the fact that relativistic wave equations have both positive and negative frequency solutions is reconciled with the requirement that a sensible quantum theory contains only positive excitation energies.
I am having a hard time deciphering the last sentence here. A negative frequency solution carries with it the creation operator: does this create a field excitation/particle that "cancels out" the negative frequency particle? I am quite lost as to what exactly is going on, physically, here. I'd like a picture in my head if possible, rather than equations!