Particles as excitation of a field

[Butch]

Getting my head around this, a particle is an excitation of its appropriate field, but what is the nature of that excitation? 

It does not wash as an oscillation, as such it would either generate a continual wave or the particle would cease to exist. It seems to me it must be a perturbation of the field extending to infinity via the inverse square... am I on the right track?