I've been trying to fill in my mathematical blanks of things I just took as dogma before. Especially, not having a background in functional analysis, the functional derivatives often seem to me mumbo jumbo whenever things go beyond the "definition for physicists". In particular I tried looking everywhere to make sense of this passage from Sterman's: I understand everything here but that last ##\equiv## . Especially what makes it look total whatever-y to me is the indices i, j on the RHS. Why does the momentum operator have j and the field i on the numerator, and the field j on the denominator? This could've been totally different and I would've equally said "mmh okay I suppose", something which worries me every time it happens. If you think it would be beneficial, on top on the answer to this specific part, a primer of functional analysis / derivatives / ? would be appreciated. Thanks.