Gauss Optics and Gauss Sum on an Optical Phenomena
Shigeki Matsutani
TL;DR
This paper explores the connection between Gauss optics and Gauss sums, linking optical phenomena with mathematical structures through the Weil representation, and revises previous work on their reciprocity and wave-particle duality.
Contribution
It introduces a new relation between Gauss optics and Gauss sums based on recent Weil representation studies, expanding understanding of their mathematical and physical interplay.
Findings
Established a link between Gauss optics and Gauss sums
Connected reciprocity of Gauss sums with wave-particle duality
Revised previous findings using Weil representation insights
Abstract
In the previous article (Found Phys. Lett. {\bf{16}} 325-341), we showed that a reciprocity of the Gauss sums is connected with the wave and particle complementary. In this article, we revise the previous investigation by considering a relation between the Gauss optics and the Gauss sum based upon the recent studies of the Weil representation for a finite group.
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