Applications to Particle and Condensed-Matter Physics

This chapter works out in detail two important applications of effective field theory for Nambu–Goldstone bosons. The chiral perturbation theory of mesons is used as a prototype of a relativistic effective field theory. The organization of the effective Lagrangian is explained in detail. The invariant Lagrangian is then worked out up to the next-to-leading order in the derivative expansion. The anomalous part of the effective Lagrangian is constructed in the special case of two light quark flavors. The discussion is rounded with several concrete applications to meson physics and the physics of dense nuclear matter. The next prototypical example is the effective field theory for spin waves in ferro- and antiferromagnets. The contrast between the two systems exposes the general distinction between power counting for type-A and type-B Nambu–Goldstone bosons. Realistic spin systems are often subject to perturbations breaking the ideal spin symmetry, and the text thus includes an extended discussion of such effects. The last section draws the reader’s attention to some peculiar properties of ferromagnets, which can be largely traced to the topology of the coset space.