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Abstract
Casimir forces arise from vacuum fluctuations. They are fully understood only for simple models, and are important in nano and microtechnologies. We report our experience of computer algebra calculations toward the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases confidence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green’s functions is at the boundatry of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that indicate the possibility of alternative regularizations. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and suggest combined numerical and symbolic approaches toward a more general computational framework.
Original language  English 

Title of host publication  Computer Mathematics 
Subtitle of host publication  9th Asian Symposium (ASCM2009), Fukuoka, December 2009, 10th Asian Symposium (ASCM2012), Beijing, October 2012, Contributed Papers and Invited Talks 
Editors  Ruyong Feng, Wenshin Lee, Yosuke Sato 
Publisher  Springer 
Pages  171180 
ISBN (Electronic)  9783662437995 
ISBN (Print)  9783662437988 
DOIs  
Publication status  Published  1 Oct 2014 
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Dive into the research topics of 'Towards the calculation of Casimir forces for inhomogeneous planar media'. Together they form a unique fingerprint.Projects
 1 Finished

A Constraint Solver Synthesiser: A Constraint Solver Synthesiser
Miguel, I. J., Balasubramaniam, D., Gent, I. P., Kelsey, T. & Linton, S. A.
1/10/09 → 30/09/14
Project: Standard