Effective Lagrangian for Nonrelativistic Systems

Understand

The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing $1$ dynamical degree of freedom by two NGB fields.

• We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives.
• We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces.
• Its consequence on the dispersion relations of the NGBs is clarified.