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首页> 外文期刊>Progress of Theoretical Physics >An application of spontaneously broken local gauge theory to molecular dynamics - An coriolis and centrifugal forces fictitious force?
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An application of spontaneously broken local gauge theory to molecular dynamics - An coriolis and centrifugal forces fictitious force?

机译：自发破裂的局部规范理论在分子动力学中的应用-科里奥利力和离心力是虚拟力吗？

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摘要

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.
机译：具有单一规格条件的自发破裂局部规格理论被应用于许多粒子系统的集体旋转和振动运动的表述。我们首先处理一个简单的例子，说明单个粒子在中心势中的运动。通过要求拉格朗日在任意随时间变化的旋转下是形式不变的，我们概括了这种旋转不变拉格朗日。通过构造协变导数进行一般化。通过协变量导数，角速度将作为局部非阿贝尔O（3）规范场获得。所得的拉格朗日值与在旋转框架中描述粒子的结果完全相同：科里奥利和离心力项出现在其中。因此，我们发现旋转框架和静止框架通过局部规格变换相互连接。我们研究了O（3）对称性自发破裂的情况，通过采用单一规范条件消除了由于这种对称性破裂而产生的Nambu-Goldstone模态，我们观察到了希格斯机制的类似物。执行了对许多粒子系统的概括。特别是，我们证明了由于O（3）对称性的自发破裂和所谓的Eckart条件（通常用于常规的分子物理学处理）而导致消除Nambu-Goldstone模式的单一规范条件的等效性。此外，确定了由平移不变性引起的其他Nambu-Goldstone模式。有关Nambu-Goldstone模态的所有明确公式都是仅使用势的不变性质导出的。

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