EFFECTIVE-FIELD THEORIES FOR QED BOUND-STATES - EXTENDING NONRELATIVISTIC QED TO STUDY RETARDATION EFFECTS - ART. NO. 093013

Nonrelativistic QED bound states are difficult to study because of the presence of at least three widely different scales: the masses, three -momenta (p(i)) and kinetic energies (K-i) of the constituents. Nonrel ativistic QED (NRQED), an effective field theory developed by Caswell and Lepage, simplifies greatly bound state calculations by eliminating the masses as dynamical scales. As we demonstrate, NRQED diagrams inv olving only photons of energy E-gamma similar or equal to p(i) contrib ute, in any calculation, to a unique order in alpha. This is not the c ase, however, for diagrams involving photons with energies E-gamma sim ilar or equal to K-i (''retardation effects''), for which no simple co unting counting rules can be given. We present an extension of NRQED i n which the contribution of those ultra-soft photons can be isolated o rder by order in alpha. This is effectively accomplished by performing a multipole expansion of the NRQED vertices. [S0556-2821(98)01121-7].