A Lagrangian description of the qubit based on Schwinger’s picture of Quantum Mechanics that allows for a Feynman-like computation of its probability amplitudes is presented. The Lagrangian is a function on the groupoid that describes the qubit and at the same time determines a self-adjoint element on its associated algebra. Feynman’s paths are replaced by histories on the groupoid which form a groupoid again, and a simple method to compute the sum over all histories is discussed. The unitarity of the theory described in this way imposes quantization conditions on the parameters determining the Lagrangian, and some particular instances are solved completely.

中文翻译：

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量子位的拉格朗日路径积分方法

提出了基于施温格量子力学图的量子位的拉格朗日描述，允许对其概率幅度进行类似费曼的计算。拉格朗日函数是群形上的一个函数，它描述了量子位，同时确定了其相关代数上的自伴元素。费曼路径被群群上的历史所取代，再次形成群群，并讨论了计算所有历史之和的简单方法。以这种方式描述的理论的幺正性对确定拉格朗日量的参数施加了量化条件，并且完全解决了一些特定情况。