On the Euclidean Version of the Photon Number Integral
نویسنده
چکیده
We reconsider the Euclidean version of the photon number integral introduced in [1]. This integral is well defined for any smooth non-selfintersecting curve in R . Besides studying general features of this integral (including its conformal invariance), we evaluate it explicitly for the ellipse. The result is nellipse = (ξ −1 + ξ)π, where ξ is the ratio of the minor and major axes. This is in agreement with the previous result ncircle = 2π 2 and also with the conjecture that the minimum value of n for any plane curve occurs for the circle.
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