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A new scaling property of the Casimir energy for a piecewise uniform string. (English) Zbl 0960.81059

Summary: An unexpected and very accurate scaling invariance of the Casimir energy of the piecewise uniform relativistic string is pointed out. The string consists of \(2N\) pieces of equal length, of alternating type I/type II material, endowed with different tensions and mass densities but adjusted such that the velocity of transverse sound equals \(c\). If \(E_N(x)\) denotes the Casimir energy as a function of the tension ratio \(x=T_{\text{I}} /T_{\text{II}}\), it turns out that the ratio \(f_N(x)= E_N(x)/E_N(0)\), which lies between zero and one, will be practically independent of \(N\) for integers \(N\geq 2\). Physical implications of this scaling invariance are discussed. Finite temperature theory is also considered.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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