  We present a relativistic procedure for the chiral expansion of the two-pion
exchange component of the $NN$ potential, which emphasizes the role of
intermediate $\pi N$ subamplitudes. The relationship between power counting in
$\pi N$ and $NN$ processes is discussed and results are expressed directly in
terms of observable subthreshold coefficients. Interactions are determined by
one- and two-loop diagrams, involving pions, nucleons, and other degrees of
freedom, frozen into empirical subthreshold coefficients. The full evaluation
of these diagrams produces amplitudes containing many different loop integrals.
Their simplification by means of relations among these integrals leads to a set
of intermediate results. Subsequent truncation to $O(q^4)$ yields the
relativistic potential, which depends on six loop integrals, representing
bubble, triangle, crossed box, and box diagrams. The bubble and triangle
integrals are the same as in $\pi N$ scattering and we have shown that they
also determine the chiral structures of box and crossed box integrals.
Relativistic threshold effects make our results to be not equivalent with those
of the heavy baryon approach. Performing a formal expansion of our results in
inverse powers of the nucleon mass, even in regions where this expansion is not
valid, we recover most of the standard heavy baryon results. The main
differences are due to the Goldberger-Treiman discrepancy and terms of
$O(q^3)$, possibly associated with the iteration of the one-pion exchange
potential.
