LEADER 05112nam 2200589Ia 450 001 9910826337903321 005 20230607222128.0 010 $a1-281-95148-X 010 $a9786611951481 010 $a981-279-994-X 035 $a(CKB)1000000000538003 035 $a(StDuBDS)AH24685505 035 $a(SSID)ssj0000132722 035 $a(PQKBManifestationID)11150682 035 $a(PQKBTitleCode)TC0000132722 035 $a(PQKBWorkID)10039129 035 $a(PQKB)11507254 035 $a(MiAaPQ)EBC1681543 035 $a(WSP)00004733 035 $a(Au-PeEL)EBL1681543 035 $a(CaPaEBR)ebr10255362 035 $a(CaONFJC)MIL195148 035 $a(OCoLC)815754671 035 $a(EXLCZ)991000000000538003 100 $a20011127d2001 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCritical properties of [Greek letter phi]4-theories$b[electronic resource] /$fHagen Kleinert, Verena Schulte-Frohlinde 210 $aRiver Edge, N.J. $cWorld Scientific$dc2001 215 $a1 online resource (512p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-02-4658-7 320 $aIncludes bibliographical references and index. 327 $aDefinition of [phi]4-Theory; Feynman Diagrams; Diagrams in Momentum Space; Structural Properties of Perturbation Theory; Diagrams for Multicomponent Fields; Scale Transformations of Fields and Correlation Functions; Regularization of Feynman Integrals; Renormalization; Renormalization Group; Recursive Subtraction of UV-Divergences via R-Operation; Zero-Mass Approach to Counterterms; Calculation of Momentum Space Integrals; Generation of Diagrams; Results of the Five-Loop Calculation; Basic Resummation Theory; Critical Exponents of O(N)-Symmetric Theory; Cubic Anisotropy; Variational Perturbation Theory; Critical Exponents from Other Expansions; New Resummation Algorithm; Conclusion: Diagrammatic R-Operation Up to Five Loops; Contributions to Renormalization-Constants. 330 8 $aThis work explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series.$bThis work explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition.;Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a method for finding recursively all Feynman diagrams to any order in the coupling strength. Algebraic computer programs are supplied on accompanying World Wide Web pages. The diagrams correspond to integrals in momentum space. They are evaluated in 4-epsilon dimensions, where they possess pole terms in 1/epsilon. The pole terms are collected into renormalization constants.;The theory of the renormalization group is used to find the critical scaling laws. They contain critical exponents which are obtained from the renormalization constants in the form of power series. These are divergent, due to factorially growing expansion coefficients. The evaluation requires resummation procedures, which are performed in two ways: (1) using traditional methods based on Pade and Borel transformations, combined with analytic mappings; (2) using modern variational perturbation theory, where the results follow from a simple strong-coupling formula. As a crucial test of the accuracy of the methods, the critical exponent alpha governing the divergence of the specific heat of superfluid helium is shown to agree very well with the extremely precise experimental number found in the space shuttle orbiting the earth (whose data are displayed on the cover of the book).;The phi4-theories investigated in this book contain any number N of fields in an O(N)-symmetric interaction, or in an interaction in which O(N)-symmetry is broken by a term of a cubic symmetry. The crossover behavior between the different symmetries is investigated. In addition, alternative ways of obtaining critical exponents of phi4-theories are sketched, such as variational perturbation expansions in three rather than 4-epsilon dimensions, and improved ratio tests in high-temperature expansions of lattice models. 606 $aPerturbation (Quantum dynamics) 606 $aPhysics 615 0$aPerturbation (Quantum dynamics) 615 0$aPhysics. 676 $a530.143 700 $aKleinert$b Hagen$052673 701 $aSchulte-Frohlinde$b Verena$01619035 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826337903321 996 $aCritical properties of 4-theories$93951078 997 $aUNINA