000 04114nam a22005895i 4500
001 978-3-319-47551-6
003 DE-He213
005 20210118123642.0
007 cr nn 008mamaa
008 161125s2017 gw | s |||| 0|eng d
020 _a9783319475516
_9978-3-319-47551-6
024 7 _a10.1007/978-3-319-47551-6
_2doi
050 4 _aQC174.45-174.52
072 7 _aPHQ
_2bicssc
072 7 _aSCI057000
_2bisacsh
072 7 _aPHS
_2thema
082 0 4 _a530.14
_223
100 1 _aYeats, Karen.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 2 _aA Combinatorial Perspective on Quantum Field Theory
_h[electronic resource] /
_cby Karen Yeats.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aIX, 120 p. 16 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Mathematical Physics,
_x2197-1757 ;
_v15
505 0 _aPart I Preliminaries -- Introduction -- Quantum field theory set up -- Combinatorial classes and rooted trees -- The Connes-Kreimer Hopf algebra -- Feynman graphs -- Part II Dyson-Schwinger equations -- Introduction to Dyson-Schwinger equations -- Sub-Hopf algebras from Dyson-Schwinger equations -- Tree factorial and leading log toys -- Chord diagram expansions -- Differential equations and the (next-to)m leading log expansion -- Part III Feynman periods -- Feynman integrals and Feynman periods -- Period preserving graph symmetries -- An invariant with these symmetries -- Weight -- The c2 invariant -- Combinatorial aspects of some integration algorithms -- Index.
520 _aThis book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
650 0 _aQuantum field theory.
650 0 _aString theory.
650 0 _aMathematical physics.
650 0 _aDiscrete mathematics.
650 1 4 _aQuantum Field Theories, String Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P19048
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
650 2 4 _aDiscrete Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M29000
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319475509
776 0 8 _iPrinted edition:
_z9783319475523
830 0 _aSpringerBriefs in Mathematical Physics,
_x2197-1757 ;
_v15
856 4 0 _uhttps://doi.org/10.1007/978-3-319-47551-6
912 _aZDB-2-PHA
999 _c446196
_d446196
942 _cEB
506 _aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506 _fOnline access from local network of NaUOA.
506 _fOnline access with authorization at https://link.springer.com/
506 _fОнлайн-доступ з локальної мережі НаУОА.
506 _fОнлайн доступ з авторизацією на https://link.springer.com/