A novel derivation of Feynman’s sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac–Feynman–Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function ℓ on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian ℓ allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman’s original derivation of the propagator for a point particle described by a classical Lagrangian L.

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施温格的量子力学图片中的费曼传播者

提出了利用量子力学的施温格图的群形描述对费曼的量子传播子的历史求和构造的新推导。结果表明，这种构造对应于称为 Dirac-Feynman-Schwinger (DFS) 状态的自然状态族的 GNS 表示。这些状态是从一个q- 拉格朗日函数ℓ关于系统配置的groupoid。构造了系统的历史群，q-拉格朗日ℓ允许我们在 groupoid 的代数上定义一个 DFS 状态。黎曼流形对的群样的特定实例用于说明费曼对经典拉格朗日描述的点粒子的传播子的原始推导大号.