Effective Lagrangians for quantum many-body systems

Understand

The low-energy and low-momentum dynamics of systems with a spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons.

• It can be conveniently encoded in a model-independent effective field theory whose structure is fixed by symmetry up to a set of effective coupling constants.
• We construct the most general effective Lagrangian for the Nambu-Goldstone bosons of spontaneously broken global internal symmetry up to the fourth order in derivatives.
• Rotational invariance and spatial dimensionality of one, two or three are assumed in order to obtain compact explicit expressions, but our method is completely general and can be applied without modifications to condensed matter systems with a discrete space group as well as to higher-dimensional theories.