000023162 001__ 23162
000023162 005__ 20140130014805.0
000023162 037__ $$9arXiv$$ahep-th/0001210$$chep-th
000023162 035__ $$9arXiv$$zoai:arXiv.org:hep-th/0001210
000023162 037__ $$aJINR-E2-2000-9
000023162 035__ $$9DESY$$zD00-05020
000023162 035__ $$9CERNKEY$$z2174083
000023162 035__ $$9SPIRESTeX$$zShirkov:1999hj
000023162 100__ $$aShirkov, Dmitrij V.$$uDubna, JINR
000023162 210__ $$aBOGOLUBOV
000023162 210__ $$aBOGOLIUBOV
000023162 210__ $$aBOGOLYUBOV
000023162 245__ $$aBogolyubov renormalization group and symmetry of solution in mathematical physics
000023162 246__ $$9arXiv$$aThe Bogoliubov renormalization group and solution symmetry in mathematical physics.
000023162 269__ $$c1999-01
000023162 300__ $$a36
000023162 500__ $$aDedicated to the memory of Boris Medvedev
000023162 520__ $$aEvolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparameterisation one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of new approach to solution for a problem of self-focusing laser beam in a non-linear medium.
000023162 690C_ $$2INSPIRE$$aConference Paper
000023162 690C_ $$2INSPIRE$$aPublished
000023162 695__ $$2INSPIRE$$atalk: Taxco 1999/01/11
000023162 695__ $$2INSPIRE$$arenormalization group: transformation
000023162 695__ $$2INSPIRE$$arenormalization group: beta function
000023162 695__ $$2INSPIRE$$asymmetry
000023162 695__ $$2INSPIRE$$ageometry
000023162 695__ $$2INSPIRE$$acritical phenomena
000023162 695__ $$2INSPIRE$$aoptics: nonlinear
000023162 695__ $$2INSPIRE$$abibliography
000023162 700__ $$aKovalev, Vladimir F.$$uMoscow, Inst. Math. Modeling
000023162 773__ $$a10.1016/S0370-1573(01)00039-4$$c219-249$$pPhys.Rept.$$v352$$y2001
000023162 773__ $$tContributed to RG-2000: Conference on Renormalization Group$$wC99/01/11.3
000023162 8564_ $$uhttp://www.adsabs.harvard.edu/abs/2001PhR...352..219S$$w2001PhR...352..219S$$yADSABS
000023162 8564_ $$uhttp://alice.cern.ch/format/showfull?sysnb=2174083$$w2174083$$yCERNKEY
000023162 8564_ $$uhttp://www.jinr.ru/publish/Preprints/2000/e2-2000-9.pdf$$w2000/e2-2000-9.pdf$$yDUBNA2
000023162 8564_ $$uhttp://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SPIRES&_method=citationSearch&_volkey=03701573%23352%23219%23&_version=1&md5=d3b0f1e6e2db32725db380d14b6d5385$$w03701573%23352%23219%23&_version=1&md5=d3b0f1e6e2db32725db380d14b6d5385$$ySCIDIR
000023162 8564_ $$uhttp://www1.jinr.ru/Preprints/2000/e2-2000-9.pdf
000023162 8564_ $$uhttp://lt-jds.jinr.ru/record/23162/files/e2-2000-9.pdf$$yFulltext
000023162 909CO $$ooai:jdsweb.jinr.ru:23162$$pglobal
000023162 961__ $$x2000-02-01
000023162 961__ $$c2005-03-30
000023162 970__ $$aSPIRES-4304500
000023162 980__ $$aPublished
000023162 980__ $$aarXiv
000023162 980__ $$aCiteable
000023162 980__ $$aReview
000023162 980__ $$aCORE
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