LEADER 00941nam a22002531i 4500 001 991003777799707536 005 20030919163537.0 008 031111s1989 uik|||||||||||||||||eng 020 $a0333325869 035 $ab12472803-39ule_inst 035 $aARCHE-050608$9ExL 040 $aDip.to Lingue$bita$cA.t.i. Arché s.c.r.l. Pandora Sicilia s.r.l. 082 04$a821.912 100 1 $aManganiello, Dominic$0199008 245 10$aT. S. Eliot and Dante /$cDominic Manganiello 260 $aBasingstoke :$bMacMillan,$c1989 300 $aX, 212 p. ;$c22 cm 600 14$aEliot, Thomas Stearns$xOpere$xInflussi di Dante Alighieri. 907 $a.b12472803$b02-04-14$c13-11-03 912 $a991003777799707536 945 $aLE012 828.91 ELI MAN$g1$i2012000229600$lle012$o-$pE0.00$q-$rl$s- $t0$u2$v2$w2$x0$y.i12904168$z13-11-03 996 $aT. S. Eliot and Dante$9182123 997 $aUNISALENTO 998 $ale012$b13-11-03$cm$da $e-$feng$guik$h0$i1 LEADER 01318nam 2200433 450 001 9910793723403321 005 20200106082244.0 010 $a1-78969-096-X 035 $a(CKB)4100000008952938 035 $a(MiAaPQ)EBC5845639 035 $a(EXLCZ)994100000008952938 100 $a20190923h20192019 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 14$aThe secret life of memorials $ethrough the memory lens of the Australian South Sea islanders /$fJulie Kaye Mitchell 210 1$aOxford :$cArchaeopress Archaeology,$d[2019] 210 4$d©2019 215 $a1 online resource (201 pages) $cillustrations (some color), charts 311 $a1-78969-095-1 320 $aIncludes bibliographical references. 606 $aPacific Islanders$zAustralia 606 $aMemorials$zAustralia 606 $aCollective memory$zAustralia 607 $aAustralia$2fast 615 0$aPacific Islanders 615 0$aMemorials 615 0$aCollective memory 676 $a994.004995 700 $aMitchell$b Julie Kaye$01579951 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793723403321 996 $aThe secret life of memorials$93860407 997 $aUNINA LEADER 07978nam 22004693 450 001 996587865503316 005 20240131215442.0 010 $a3-031-46987-9 035 $a(CKB)29527082000041 035 $a(MiAaPQ)EBC31063558 035 $a(Au-PeEL)EBL31063558 035 $a(OCoLC)1416698436 035 $a(EXLCZ)9929527082000041 100 $a20240115d2024 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aScattering Amplitudes in Quantum Field Theory 205 $aFirst edition. 210 1$aCham :$cSpringer International Publishing AG,$d2024. 210 4$d©2024. 215 $a1 online resource (312 pages) 225 1 $aLecture Notes in Physics Series ;$vv.1021 311 $a3-031-46986-0 327 $aIntro -- Preface -- Acknowledgements -- Contents -- Acronyms -- 1 Introduction and Foundations -- 1.1 Poincaré Group and Its Representations -- 1.2 Weyl and Dirac Spinors -- 1.3 Non-Abelian Gauge Theories -- 1.4 Feynman Rules for Non-Abelian Gauge Theories -- 1.5 Scalar QCD -- 1.6 Perturbative Quantum Gravity -- 1.7 Feynman Rules for Perturbative Quantum Gravity -- 1.8 Spinor-Helicity Formalism for Massless Particles -- 1.9 Polarisations of Massless Particles of Spin 12, 1 and 2 -- 1.10 Colour Decompositions for Gluon Amplitudes -- 1.10.1 Trace Basis -- 1.10.2 Structure Constant Basis -- 1.11 Colour-Ordered Amplitudes -- 1.11.1 Vanishing Tree Amplitudes -- 1.11.2 The Three-Gluon Tree-Amplitudes -- 1.11.3 Helicity Weight -- 1.11.4 Vanishing Graviton Tree-Amplitudes -- References -- 2 On-Shell Techniques for Tree-Level Amplitudes -- 2.1 Factorisation Properties of Tree-Level Amplitudes -- 2.1.1 Collinear Limits -- 2.1.2 Soft Theorems -- 2.1.3 Spinor-Helicity Formulation of Soft Theorems -- 2.1.4 Subleading Soft Theorems -- 2.2 BCFW Recursion for Gluon Amplitudes -- 2.2.1 Large z Falloff -- 2.3 BCFW Recursion for Gravity and Other Theories -- 2.4 MHV Amplitudes from the BCFW Recursion Relation -- 2.4.1 Proof of the Parke-Taylor Formula -- 2.4.2 The Four-Graviton MHV Amplitude -- 2.5 BCFW Recursion with Massive Particles -- 2.5.1 Four-Point Amplitudes with Gluons and MassiveScalars -- 2.6 Symmetries of Scattering Amplitudes -- 2.7 Double-Copy Relations for Gluon and Graviton Amplitudes -- 2.7.1 Lower-Point Examples -- 2.7.2 Colour-Kinematics Duality: A Four-Point Example -- 2.7.3 The Double-Copy Relation -- References -- 3 Loop Integrands and Amplitudes -- 3.1 Introduction to Loop Amplitudes -- 3.2 Unitarity and Cut Construction -- 3.3 Generalised Unitarity -- 3.4 Reduction Methods -- 3.4.1 Tensor Reduction. 327 $a3.4.2 Transverse Spaces and Transverse Integration -- 3.5 General Integral and Integrand Bases for One-Loop Amplitudes -- 3.5.1 The One-Loop Integral Basis -- 3.5.2 A One-Loop Integrand Basis in Four Dimensions -- 3.5.2.1 The Box Integrand in Four Dimensions -- 3.5.2.2 The Triangle Integrand in Four Dimensions -- 3.5.2.3 The Bubble Integrand in Four Dimensions -- 3.5.3 D-Dimensional Integrands and Rational Terms -- 3.5.3.1 The Pentagon Integrand -- 3.5.3.2 Extending the Box, Triangle and Bubble Integrand Basis to D=4-2? Dimensions -- 3.5.4 Final Expressions for One-Loop Amplitudes in D-Dimensions -- 3.5.5 The Direct Extraction Method -- 3.6 Project: Rational Terms of the Four-Gluon Amplitude -- 3.7 Outlook: Rational Representations of the External Kinematics -- 3.8 Outlook: Multi-Loop Amplitude Methods -- References -- 4 Loop Integration Techniques and Special Functions -- 4.1 Introduction to Loop Integrals -- 4.2 Conventions and Basic Methods -- 4.2.1 Conventions for Minkowski-Space Integrals -- 4.2.2 Divergences and Dimensional Regularisation -- 4.2.3 Statement of the General Problem -- 4.2.4 Feynman Parametrisation -- 4.2.5 Summary -- 4.3 Mellin-Barnes Techniques -- 4.3.1 Mellin-Barnes Representation of the One-Loop Box Integral -- 4.3.2 Resolution of Singularities in ? -- 4.4 Special Functions, Differential Equations, and Transcendental Weight -- 4.4.1 A First Look at Special Functionsin Feynman Integrals -- 4.4.2 Special Functions from Differential Equations: The Dilogarithm -- 4.4.3 Comments on Properties of the Defining Differential Equations -- 4.4.4 Functional Identities and Symbol Method -- 4.4.5 What Differential Equations Do Feynman Integrals Satisfy? -- 4.5 Differential Equations for Feynman Integrals -- 4.5.1 Organisation of the Calculation in Terms of Integral Families -- 4.5.2 Obtaining the Differential Equations. 327 $a4.5.3 Dimensional Analysis and Integrability Check -- 4.5.4 Canonical Differential Equations -- 4.5.5 Solving the Differential Equations -- 4.6 Feynman Integrals of Uniform Transcendental Weight -- 4.6.1 Connection to Differential Equationsand (Unitarity) Cuts -- 4.6.2 Integrals with Constant Leading Singularities and Uniform Weight Conjecture -- References -- 5 Solutions to the Exercises -- Exercise 1.1: Manipulating Spinor Indices -- Exercise 1.2: Massless Dirac Equation and Weyl Spinors -- Exercise 1.3: SU(Nc) Identities -- Exercise 1.4: Casimir Operators -- Exercise 1.5: Spinor Identities -- Exercise 1.6: Lorentz Generators in the Spinor-Helicity Formalism -- Exercise 1.7: Gluon Polarisations -- Exercise 1.8: Colour-Ordered Feynman Rules -- Exercise 1.9: Independent Gluon Partial Amplitudes -- Exercise 1.10: The MHV3 Amplitude -- Exercise 1.11: Four-Point Quark-Gluon Scattering -- Exercise 2.1: The Vanishing Splitting Function Splittree+(x,a+,b+) -- Exercise 2.2: Soft Functions in the Spinor-Helicity Formalism -- Exercise 2.3: A qggg Amplitude from Collinear and Soft Limits -- Exercise 2.4: The Six-Gluon Split-Helicity NMHV Amplitude -- Exercise 2.5: Soft Limit of the Six-Gluon Split-Helicity Amplitude -- Exercise 2.6: Mixed-Helicity Four-Point Scalar-Gluon Amplitude -- Exercise 2.7: Conformal Algebra -- Exercise 2.8: Inversion and Special Conformal Transformations -- Exercise 2.9: Kinematical Jacobi Identity -- Exercise 2.10: Five-Point KLT Relation -- Exercise 3.1: The Four-Gluon Amplitude in N=4 Super-Symmetric Yang-Mills Theory -- Exercise 3.2: Quadruple Cuts of Five-Gluon MHV Scattering Amplitudes -- Exercise 3.3: Tensor Decomposition of the Bubble Integral -- Exercise 3.4: Spurious Loop-Momentum Space for the Box Integral -- Exercise 3.5: Reducibility of the Pentagon in Four Dimensions -- Exercise 3.6: Parametrising the Bubble Integrand. 327 $aExercise 3.7: Dimension-Shifting Relation at One Loop -- Exercise 3.8: Projecting Out the Triangle Coefficients -- Exercise 3.9: Rank-One Triangle Reduction with Direct Extraction -- Exercise 3.10: Momentum-Twistor Parametrisations -- Exercise 4.1: The Massless Bubble Integral -- Exercise 4.2: Feynman Parametrisation -- Exercise 4.3: Taylor Series of the Log-Gamma Function -- Exercise 4.4: Finite Two-Dimensional Bubble Integral -- Exercise 4.5: Laurent Expansion of the Gamma Function -- Exercise 4.6: Massless One-Loop Box with Mellin-Barnes Parametrisation -- Exercise 4.7: Discontinuities -- Exercise 4.8: The Symbol of a Transcendental Function -- Exercise 4.9: Symbol Basis and Weight-Two Identities -- Exercise 4.10: Simplifying Functions Using the Symbol -- Exercise 4.11: The Massless Two-Loop Kite Integral -- Exercise 4.13: ``d log'' Form of the Massive Bubble Integrand with D=2 -- Exercise 4.14: An Integrand with Double Poles: The Two-Loop Kite in D=4 -- Exercise 4.16: The Box Integrals with the Differential Equations Method -- References -- A Conventions and Useful Formulae -- Reference. 410 0$aLecture notes in physics 700 $aBadger$b Simon$01585517 701 $aHenn$b Johannes M$01017317 701 $aPlefka$b Jan C$01585518 701 $aZoia$b Simone$01231763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996587865503316 996 $aScattering Amplitudes in Quantum Field Theory$93870695 997 $aUNISA