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Particles as excitation of a field

Butch
in Quantum Theory

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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?

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