Prog. Theor. Phys. Vol. 98 No. 2 (1997) pp. 283-298

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Invited Papers

An Application of Spontaneously Broken Local Gauge Theory to Molecular Dynamics

— Are Coriolis and Centrifugal Forces Fictitious Force? —

Haruo Ui

Department of Physics, Hiroshima University, Higashi-Hiroshima 739

(Received December 16, 1996)

Abstract:

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. Through the covariant derivative, the angular velocity is obtained as a local nonabelian O(3) gauge field. The resulting Lagrangian is precisely the same as that describing the particle in a rotating frame; Coriolis and centrifugal force 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 arising as a result of this symmetry breaking, we observe an analogue of the Higgs mechanism. Generalization to many particle systems is performed. In particular, we prove the equivalence of the unitary gauge condition imposed to eliminate the Nambu-Goldstone modes due to the spontaneous breakdown of the O(3) symmetry and the so-called Eckart condition, usually employed in conventional treatments of molecular physics. 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.

URL : http://ptp.ipap.jp/link?PTP/98/283/
DOI : 10.1143/PTP.98.283

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