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This 2010 paper **by S.J. Brodsky and P. Hoyer** shows 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.''