Recently I learned functional integral's formalism in QFT. I have realized that I don't understand why exactly do we introduce it. We have the expression for $S$-matrix, then we may rewrite it in through functional integral.

But why do we use functional integration? I read that it helps to "conserve" gauge symmetries for massless fields and that it avoids infinite results after integration through integnal lines. But these are formal arguments. I don't understand it clearly.

Can you add some information which can help me?

This post imported from StackExchange Physics at 2014-08-11 14:53 (UCT), posted by SE-user Andrew McAddams