On the Foundations of Chiral Perturbation Theory

TL;DR

This work establishes a rigorous foundation for chiral perturbation theory by deriving an effective Lagrangian for Goldstone bosons from the Ward identities of the underlying Lorentz-invariant theory. It shows that, in the absence of anomalies, the generating functional becomes gauge invariant and the low-energy dynamics can be captured by a derivative-expanded EFT on the G/H coset with a leading O(p^2) Lagrangian defined by a metric on G/H and Killing vectors that encode current couplings. The analysis provides an invariance theorem proving that the effective Lagrangian can be rewritten in a manifestly gauge-invariant form to all orders, with anomalies incorporated via a Wess–Zumino term if present. It then extends the framework to higher orders and approximate symmetries, offering a coherent bridge between current algebra/PCAC and modern EFT techniques, and highlighting the indispensable role of Lorentz invariance in these results.

Abstract

The properties of the effective field theory relevant for the low energy structure generated by the Goldstone bosons of a spontaneously broken symmetry are reexamined. It is shown that anomaly free, Lorentz invariant theories are characterized by a gauge invariant effective Lagrangian, to all orders of the low energy expansion. The paper includes a discussion of anomalies and approximate symmetries, but does not cover nonrelativistic effective theories.