August 1997 Progress of Theoretical Physics Vol. Haruo Ui pp. 283-298 Spontaneously broken local gauge theory with the unitary gauge condition is applied to a formulation of collective rotation and vibration motion of many particle systems. We first treat a simple example of the motion of single particle in a central potential. We generalize this rotation invariant Lagrangian by requiring the Lagrangian to be form invariant under an arbitrary time-dependent rotation.
Generalization is made by constructing a covariant derivative.
We thus find that the rotating and rest frames are mutually connected by the local gauge transformation. By adopting the unitary gauge condition which eliminates Nambu-Goldstone modes arising as a result of this symmetry breaking, we observe an analogue of the Higgs mechanism. Generalization to many particle systems is performed. In addition, the other Nambu-Goldstone modes arising from translational invariance are determined. All the explicit formulas concerning Nambu-Goldstone modes are derived using invariant property of potential alone.