AN APPLICATION OF SPONTANEOUSLY BROKEN LOCAL GAUGE-THEORY TO MOLECULAR-DYNAMICS - AN CORIOLIS AND CENTRIFUGAL FORCES FICTITIOUS FORCE

Spontaneously broken local gauge theory with the unitary gauge conditi on is applied to a formulation of collective rotation and vibration mo tion of many particle systems. We first treat a simple example of the motion of single particle in a central potential. We generalize this r otation invariant Lagrangian by requiring the Lagrangian to be form in variant under an arbitrary time-dependent rotation. Generalization is made by constructing a covariant derivative. Through the covariant der ivative, the angular velocity is obtained as a local nonabelian O(3) g auge field. The resulting Lagrangian is precisely the same as that des cribing the particle in a rotating frame: Coriolis and centrifugal for ce terms appear in it. We thus find that the rotating and rest frames are mutually connected by the local gauge transformation. We study the case in which the O(3) symmetry is spontaneously broken, By adopting the unitary gauge condition which eliminates Nambu-Goldstone modes ari sing as a result of this symmetry breaking, we observe an analogue of the Higgs mechanism. Generalization to many particle systems is perfor med. In particular, we prove the equivalence of the unitary gauge cond ition imposed to eliminate the Nambu-Goldstone modes due to the sponta neous breakdown of the O(3) symmetry and the so-called Eckart conditio n, usually employed in conventional treatments of molecular physics. I n 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 alo ne.