Abstract
The success of PCAC and current algebra more than a decade ago was an important constraint on field-theoretic attempts to construct a realistic model of the strong interactions. Our best candidate, quantum chromodynamics (QCD), satisfies part of this requirement: Gell-Mann’s current commutators are valid for renormalized operators of the fully interacting theory. What is not clear is how to realize the approximate chiral SU(n)x SU(n) symmetry of the QCD Hamiltonian in the Nambu-Goldstone mode. The hadronic ground state (vacuum) should yield expectation values of quark mass operators which do not vanish in the chiral limit; for example, we should find
for the up quark u. It is difficult to find a systematic expansion of the QCD generating functional in which the leading approximation exhibits the property (1.1). However, some progress can be made by assuming (1.1) to be true; then generally valid equations such as anomalous Ward identities give conditions which must be satisfied by any self-consistent expansion of QCD.
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Crewther, R.J. (1980). Chiral Properties of Quantum Chromodynamics. In: Rühl, W. (eds) Field Theoretical Methods in Particle Physics. NATO Advanced Study Institutes Series, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3722-5_21
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