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020 _a9783642294051
_9978-3-642-29405-1
024 7 _a10.1007/978-3-642-29405-1
_2doi
050 4 _aQC5.53
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.15
_223
100 1 _aElizalde, Emilio.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTen Physical Applications of Spectral Zeta Functions
_h[electronic resource] /
_cby Emilio Elizalde.
250 _a2nd ed. 2012.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2012.
300 _aXIV, 227 p. 14 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v855
505 0 _aIntroduction and Outlook -- Mathematical Formulas Involving the Different Zeta Functions -- A Treatment of the Non-Polynomial Contributions: Application to Calculate Partition Functions of Strings and Membranes -- Analytical and Numerical Study of Inhomogeneous Epstein and Epstein-Hurwitz Zeta Functions -- Physical Application: the Casimir Effect -- Five Physical Applications of The Inhomogeneous Generalized Epstein-Hurwitz Zeta Functions -- Miscellaneous Applications Combinig Zeta With Other Regularization Procedures -- Applications to Gravity, Strings and P-Branes -- Eleventh Application: Topological Symmetry Breaking in Self-Interacting Theories -- Twelth Application: Cosmology and The Quantum-Vacuum -- References -- Index.
520 _aZeta-function regularization is a powerful method in perturbation theory. This book is meant as a guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice (e.g. Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, noncommutative spacetime). The formulas some of which are new can be used for physically meaningful, accurate numerical calculations.  The book is to be considered as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice.   This thoroughly revised, updated and expanded edition includes in particular new explicit formulas on the general quadratic, Chowla-Selberg series case, an interplay with the Hadamard calculus, and features a new chapter on recent cosmological applications including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models.
650 0 _aMathematical physics.
650 1 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
650 2 4 _aQuantum Field Theories, String Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P19048
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642294068
776 0 8 _iPrinted edition:
_z9783642294044
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v855
856 4 0 _uhttps://doi.org/10.1007/978-3-642-29405-1
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c11833
_d11833