  Employing induced representations of the Lorentz group (Wigner's little group
construction), formalism for constructing heavy particle effective Lagrangians
is developed, and Lagrangian constraints enforcing Lorentz invariance of the S
matrix are derived. The relationship between Lorentz invariance and
reparameterization invariance is established and it is shown why a standard
ansatz for implementing reparameterization invariance in heavy fermion
effective Lagrangians breaks down at order 1/M^4. Formalism for fields of
arbitrary spin and for self-conjugate fields is presented, and the extension to
effective theories of massless fields is discussed.
