Background-Field Formalism in Quantum Systems

Abstract

The background-field formalism is used extensively in fundamental approaches to QCD to explore hadronic matrix elements of various currents. While the lattice QCD approach is formulated in the fully-interacting Hilbert space, which includes both QCD and background field interactions, the QCD sum-rule formalism is traditionally developed in the pure-QCD Hilbert space. The latter approach encounters difficulties with excited state contaminations which are not exponentially suppressed and requires extrapolations to isolate the desired physics. Proponents of the pure-QCD Hilbert space formalism used in the QCD sum-rule approach have criticized the lattice QCD approach as neglecting important physics. In this letter, the equivalence of the two approaches is established and the flaws in the former criticisms are resolved. Finally, the application of the fully-interacting Hilbert space formalism to the study of electromagnetic polarizabilities is outlined.

9 pages. Revised version accepted for publication. This and related papers may also be obtained from http://www.phys.washington.edu/~derek/Publications.html#LatticeQCD

References in corpus (4)

• QCD Sum Rules for Skeptics
• Baryon QCD sum rules in an external isovector-scalar field and baryon isospin mass splittings
• the Three-Point Vertex of Hadron Interaction with External Fields in QCD Sum Rules
• Light Hadron Masses on Coarse Lattices with Improved Actions

Cited by in corpus (19)

• Nucleon electromagnetic form factors
• QCD Sum Rules for Skeptics
• Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD
• Magnetic properties of the nucleon in a uniform background field
• Flavour singlet physics in lattice QCD with background fields
• Finite-volume and partial quenching effects in the magnetic polarizability of the neutron
• Pion magnetic polarisability using the background field method
• Magnetic polarisability of the nucleon using a Laplacian mode projection
• Neutron magnetic polarisability with Landau mode operators
• Pion Polarizabilities and Volume Effects in Lattice QCD
• Magnetic Moment of the ${\Omega }^{-}$ in QCD sumrule (QCDSR)
• Pion in a uniform background magnetic field with clover fermions
• Current Renormalization in Finite Volume
• Wave Functions of the Proton Ground State in the Presence of a Uniform Background Magnetic Field in Lattice QCD
• New QCD Sum Rules for Nucleon Axial Vector Coupling Constants
• Chiral extrapolation of the charged-pion magnetic polarizability with Padé approximant
• A Note on the External-Field Method in QCD Sum Rules
• Chiral extrapolation of the magnetic polarizability of the neutral pion
• Background field Landau mode operators for the nucleon