On the Euclidean version of the photon number integral.

Authors :: Ruijsenaars, S.
Stodolsky, L.
Source :: Journal of Mathematical Physics; Feb2008, Vol. 49 Issue 2, p023502, 10p, 1 Diagram
Publication Year :: 2008
Abstract: We reconsider the Euclidean version of the photon number integral introduced by Stodolsky [Acta Phys. Pol. B 33, 2659 (2002), e-print hep-th/02053131].This integral is well defined for any smooth non-self-intersecting curve in R<superscript>N</superscript>. Besides studying general features of this integral (including its conformal invariance), we evaluate it explicitly for the ellipse. The result is n<subscript>ellipse</subscript>=(ξ<superscript>-1</superscript>+ξ)π<superscript>2</superscript>, where ξ is the ratio of the minor and major axes. This is in agreement with the previous result n<subscript>circle</subscript>=2π<superscript>2</superscript> and also with the conjecture that the minimum value of n for any plane curve occurs for the circle. [ABSTRACT FROM AUTHOR]