Prog. Theor. Phys. Vol. 98 No. 2 (1997) pp. 283-298
An Application of Spontaneously Broken Local Gauge Theory to Molecular Dynamics
— Are Coriolis and Centrifugal Forces Fictitious Force?
Department of Physics, Hiroshima University, Higashi-Hiroshima 739
(Received December 16, 1996)
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
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.
DOI : 10.1143/PTP.98.283
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