The current algebra identity in the σ-model

• Published in: Annals of physics 1970, Vol.56 (1), p.172-197
• Main Author: Triantis, F.A
• Format: Article
• Language: English
• Subjects: CURRENT ALGEBRA/meson ($pi$) interactions with vector currents and axial-vector currents and meson ($pi$) production by axial-vector current in sigma model; CURRENTS ALGEBRA; ELEMENTARY PARTICLE MODELS/sigma model without nucleons for current algebra identity and amplitudes of meson ($pi$) interactions with vector currents and axial-vector currents and meson ($pi$) production by axial-vector currents; INTERACTIONS; MATHEMATICS; MESONS ($pi$)/ interactions with vector currents and axial-vector currents, sigma model without nucleons for current algebra identity for amplitudes of; MESONS ($pi$)/production by axial-vector current, sigma model without nucleons for current algebra identity for amplitude of; N34220 -Physics (High Energy)-Particle Interactions & Properties (Theoretical)-Electromagnetic; N34230 -Physics (High Energy)-Particle Interactions & Properties (Theoretical)-Weak; NUCLEONS; PARTICLE MODELS; PIONS; PRODUCTION; VECTORS
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/0003-4916(70)90009-6

It is shown explicitly within the σ-model without nucleons and to any order in perturbation theory that the pion-vector current and the pion-axial vector current amplitudes satisfy the current algebra identity. The amplitude for pion production by an axial vector current satisfies a supplemented identity which includes terms arising from subtraction constants in the invariant amplitudes involved. The role of PCAC is investigated, and it is found that the generalized Ward identity is sufficient but not necessary for the current algebra identity to hold.