I have lots of blooming peonies.  Can I cut back their foliage

Not if you want lots of blooms again next year.  In fact if you want
more bloom, or even just as much, you should dead-head the spent
flowers to encourage even more foliage production.  Cut them back only
after the foliage begins to yellow in the fall.

Search - none really

Your researcher is an Ohio state certified master gardener.

But if you want to verify what I've said:
http://shop.store.yahoo.com/nga-gardenshop/peony-l-g.html - "All about Peonies"

Cheers
digsalot