We consider how vectorial aspects (polarization) of light propagation can be implemented and their origin within a Feynman path integral approach. A key part of this scheme is in generalizing the standard optical path length integral from a scalar to a matrix quantity. Reparametrization invariance along the rays allows a covariant formulation where propagation can take place along a general curve. A general gradient index background is used to demonstrate the scheme. This affords a description of classical imaging optics when the polarization aspects may be varying rapidly and cannot be neglected.

中文翻译：

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电磁场的射线波二象性：经典矢量成像的费曼路径积分方法

我们考虑如何实现光传播的矢量方面（偏振）以及它们在费曼路径积分方法中的起源。该方案的一个关键部分是将标准光路长度积分从标量推广到矩阵量。沿射线的重新参数化不变性允许协变公式，其中传播可以沿一般曲线发生。一般梯度索引背景用于演示该方案。当偏振方面可能快速变化并且不能被忽略时，这提供了经典成像光学的描述。