  We show how expansions in powers of Planck's constant hbar = h/2\pi can give
new insights into perturbative and nonperturbative properties of quantum field
theories. Since hbar is a fundamental parameter, exact Lorentz invariance and
gauge invariance are maintained at each order of the expansion. The physics of
the hbar expansion depends on the scheme; i.e., different expansions are
obtained depending on which quantities (momenta, couplings and masses) are
assumed to be independent of hbar. We show that if the coupling and mass
parameters appearing in the Lagrangian density are taken to be independent of
hbar, then each loop in perturbation theory brings a factor of hbar. In the
case of quantum electrodynamics, this scheme implies that the classical charge
e, as well as the fine structure constant are linear in hbar. The connection
between the number of loops and factors of hbar is more subtle for bound states
since the binding energies and bound-state momenta themselves scale with hbar.
The hbar expansion allows one to identify equal-time relativistic bound states
in QED and QCD which are of lowest order in hbar and transform dynamically
under Lorentz boosts. The possibility to use retarded propagators at the Born
level gives valence-like wave-functions which implicitly describe the sea
constituents of the bound states normally present in its Fock state
representation.
