Bernhard Riemann, a(rche)typical mathematical-physicist?

Frontiers in Physics

Emilio eElizalde¹ 

[1] CSIC;

关键词: Interdisciplinary;    gravity;    general relativity;    mathematical physics;    Bernhard Riemann;    Physics vs Mathematics;   

DOI  :  10.3389/fphy.2013.00011

来源: DOAJ

【 摘 要 】

The work of Bernhard Riemann is discussed under the perspective ofpresent day mathematics and physics, and with a prospective view towards thefuture, too. Against the (unfortunately rather widespread) trend---which predominantly dominated national scientific societies in Europe during the last Century---of strictly classifying the work ofscientists with the aim to constrain them to separated domains of knowledge,without any possible interaction among those and often evenfighting against each other (and which, no doubt, was in part responsible forthe decline of European in favor of American science),it will be here argued, using Riemann as a model, archetypical example, that good research transcends any classification.Its uses and applications arguably permeate all domains, subjects and disciplines one can possibly define, to the point that it can be considered to be universally useful.After providing a very concise review of the main publications of Bernhard Riemann on physical problems, someconnections between Riemann's papers and contemporary physics will be considered:(i) the uses of Riemann's work on the zeta function for devising applications to the regularization of quantum field theories in curved space-time, in particular, of quantum vacuum fluctuations;(ii) the uses of the Riemann tensor in general relativity and in recentgeneralizations of this theory, which aim at understanding thepresently observed acceleration of the universe expansion (the dark energy issue).Finally, it will be argued that mathematical physics, which was yet not long ago a model paradigm for interdisciplinary activity---and had a very important pioneering role in this sense---is now quicklybeing surpassed by the extraordinarily fruitful interconnections which seem to pop up from nothing every day and simultaneously involve several disciplines, in the classical sense, includinggenetics, combinatorics, nanoelectronics, biochemistry, medicine, and even ps

【 授权许可】

Unknown