The $\hbar$ Expansion in Quantum Field Theory

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We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} 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 {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each ... continued below

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7 pages

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Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul & /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys. October 27, 2010.

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We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} 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 {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} 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.

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7 pages

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  • Journal Name: Phys.Rev.D83:045026,2011

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  • Report No.: SLAC-PUB-14224
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 992907
  • Archival Resource Key: ark:/67531/metadc1012730

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Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • October 27, 2010

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  • Oct. 14, 2017, 8:36 a.m.

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  • Nov. 2, 2017, 8:12 p.m.

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Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul & /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys. The $\hbar$ Expansion in Quantum Field Theory, article, October 27, 2010; [California]. (digital.library.unt.edu/ark:/67531/metadc1012730/: accessed July 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.