Where did the main (anti)commutation relation go?

From: MM (mikem_at_despammed.com)
Date: 09/24/04 

Date: Fri, 24 Sep 2004 14:22:08 +0000 (UTC)

In the path integral formulation of QFT for bosons,
the canonical commutations relations are not
even mentioned. (Ref: Peskin & Schroeder, ch9).

For fermions, P&S say that we must introduce
anticommuting Grassman numbers. OK, but
what about an anti-commutation relation corresponding
to {a_k, a*_k'} = i delta(k - k') ? I don't see
anything about that. Only the boring ones like
ab + ba = 0.

Similarly, for phi^4 theory (P&S pp284-289) I
don't see anything about how phi^dot doesn't
commute with phi, which is the case in the
canonical approach. Then, to derive the
phi^4 Feynman rules on p289, P&S do the
following (see the 2nd unnumbered eqn on p289):

  exp[i Integral L] = exp[i Integral L_0] exp[i Integral L_int]

             ~ exp[i Integral L_0] (1 - i Integral lambda/4! phi^4)

But L_0 contains phi^dot which doesn't commute with phi (at least,
that's what happens in the canonical formalism). The first step
above is not valid if L_0 doesn't commute with L_int. And
[L_0, L_int] is O(lambda), so it should appear in the O(lambda)
expansion. I.e: there should be a delta fn at O(lamda). Actually,
there's probably more delta fns, because higher order
Baker-Campbell-Hausdorf terms like [L_0, [L_0, L_int]] are
also O(lambda).

What am I missing?

TIA,

- MikeM.