Effective Field Theories from QCD

TL;DR

This paper introduces a method to derive effective Lagrangians from QCD by rewriting the theory in terms of collective fields, capturing long-distance physics explicitly, exemplified by a field with $ ext{eta'}$-meson quantum numbers.

Contribution

It presents a novel approach to extract effective Lagrangians from QCD using collective fields, emphasizing long-distance degrees of freedom.

Findings

Derived effective Lagrangians explicitly include long-distance degrees of freedom.

Introduced a collective field with quantum numbers of the $ ext{eta'}$-meson.

Method demonstrated through a specific example in QCD.

Abstract

We present a method for extracting effective Lagrangians from QCD. The resulting effective Lagrangians are based on exact rewrites of cut-off QCD in terms of these new collective field degrees of freedom. These cut-off Lagrangians are thus ``effective'' in the sense that they explicitly contain some of the physical long-distance degrees of freedom from the outset. As an example we discuss the introduction of a new collective field carrying the quantum numbers of the $\eta'$-meson. (Contribution presented by R. Sollacher at the workshop ``QCD'94'', Montpellier, France, July 7-13, 1994. To appear in those proceedings.)