Casimir Energy of 5D Electromagnetism and New Regularization Based on Minimal-Area Principle(Particles and Fields)
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概要
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We examine the Casimir energy of 5D electromagnetism from the recent standpoint. The bulk geometry is flat. The Z_2 symmetry and periodic property, for the extra coordinate, are taken into account. After confirming the consistency with the past result, we do new things based on a new regularization. In the treatment of the divergences, we introduce IR and UV cutoffs and restrict the (4D momentum, extra coordinate)-integral region. The regularized configuration is the sphere lattice, in the 4D continuum space, which changes along the extra coordinate. The change (renormalization flow) is specified by the minimal area principle; hence, this regularization configuration is stringlike. We do the analysis not in the Kaluza-Klein expanded form but in a closed form. We do not use any perturbation. The formalism is based on the heat-kernel approach using the position/momentum propagator. Interesting relations between the heat kernels and the P/M propagators are obtained, where we introduce the generalized P/M propagators. A useful expression of the Casimir energy, in terms of the P/M propagator, is obtained. The restricted region approach is replaced by the weight-function approach in the latter-half description. Its meaning, in relation to space-time quantization, is argued. Finite Casimir energy is numerically obtained. The compactification-size parameter (periodicity) suffers from the renormalization effect. Numerical evaluation is exploited. In particular, the minimal surface lines in the 5D flat space are obtained both numerically using the Runge-Kutta method and analytically using a general solution.
- 理論物理学刊行会の論文
- 2009-04-25
著者
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Ichinose Shoichi
Laboratory Of Physics School Of Food And Nutritional Sciences University Of Shizuoka
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ICHINOSE Shoichi
Laboratory of Physics, School of Food and Nutritional Sciences, University of Shizuoka