Hard-Pion Current-Algebra Calculation of Meson Processes—-Point Functions
- 25 November 1968
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 175 (5), 1802-1819
- https://doi.org/10.1103/physrev.175.1802
Abstract
Hard-pion techniques are presented for calculating products of an arbitrary number of vector and axial-vector currents under the assumptions of single -, -, -, and -meson saturation of intermediate sums, chiral -algebra commutation relations, conservation of vector current (CVC), and partial conservation of axial-vector current (PCAC). The single-meson dominance hypothesis is shown to imply that one calculates the products, keeping only certain generalized tree and seagull diagrams. Alternatively, the assumption can be replaced by requiring that one calculate with an "effective" interaction Lagrangian to lowest nonvanishing order. The conditions that the remaining hypotheses (current commutation relations, CVC, and PCAC) impose on are expressed in terms of functional differential equations to determine the form of . These equations are shown to be consistent with each other and may in fact be integrated order by order. The needed to calculate any four-point function is given explicitly.
Keywords
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