Minimization problem on the action given by the Lagrangean is studied on the tangent bundle over a real Hilbert space. The existence of minimizers is proved by a compactness argument. The uniqueness of classical paths is proved under quadratic potentials.

中文翻译：

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二次势下经典路径的存在与唯一性

在实际希尔伯特空间上的切线束上研究了拉格朗日给出的作用的最小化问题。紧致性论证证明了最小化器的存在。经典路径的唯一性在二次势下得到证明。