论文标题

在多重连接的配置空间中的路径积分(50年后)

Path integrals in a multiply-connected configuration space (50 years after)

论文作者

Mouchet, Amaury

论文摘要

Schulman(1968),Laidlaw&Morette-Dewitt(1971)和Dowker(1972)根据50年前提出的提案将繁殖器分解为根据同型路径类别的类别,这是一个很大的突破:它显示了Feynman功能积分如何在配置空间中Quantum Properties of Protight opprication of the配置空间打开了直接的窗口。本文对这一系列论文及其众多追随者提出的论点进行了批判性观察,以阐明为什么第一个同型组的统一线性表示的出现不仅足够而且是必要的。

The proposal made 50 years ago by Schulman (1968), Laidlaw & Morette-DeWitt (1971) and Dowker (1972) to decompose the propagator according to the homotopy classes of paths was a major breakthrough: it showed how Feynman functional integrals opened a direct window on quantum properties of topological origin in the configuration space. This paper casts a critical look at the arguments brought by this series of papers and its numerous followers in an attempt to clarify the reason why the emergence of the unitary linear representation of the first homotopy group is not only sufficient but also necessary.

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