Question

Why do we use functional integration in QFT?

Answer 1

Recently I learned functional integral's formalism in quantum field theory. I have realized that I don't understand why exactly do we introduce it. We have the expression for S" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">SS-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 internal lines. But these are formal arguments. I don't understand it clearly