Quantum Field Theory And The Standard Model: Field Theory: 1. Microscopic Theory Of Radiation; 2. Lorentz Invariance And Second Quantization; 3. Classical Field Theory; 4. Old-fashioned Perturbation Theory; 5. Cross Sections And Decay Rates; 6. The S-matr

Providing A Comprehensive Introduction To Quantum Field Theory, This Textbook Covers The Development Of Particle Physics From Its Foundations To The Discovery Of The Higgs Boson. Its Combination Of Clear Physical Explanations, With Direct Connections To Experimental Data, And Mathematical Rigor Make The Subject Accessible To Students With A Wide Variety Of Backgrounds And Interests. Assuming Only An Undergraduate-level Understanding Of Quantum Mechanics, The Book Steadily Develops The Standard Model And State-of-the Art Calculation Techniques. It Includes Multiple Derivations Of Many Important Results, With Modern Methods Such As Effective Field Theory And The Renormalization Group Playing A Prominent Role. Numerous Worked Examples And End-of-chapter Problems Enable Students To Reproduce Classic Results And To Master Quantum Field Theory As It Is Used Today. Based On A Course Taught By The Author Over Many Years, This Book Is Ideal For An Introductory To Advanced Quantum Field Theory Sequence Or For Independent Study-- Lorentz Invariance And Second Quantization In The Previous Chapter, We Saw That By Treating Each Mode Of Electromagnetic Radiation In A Cavity A Simple Harmonic Oscillator, We Can Derive Einstein's Relation Between The Coefficients Of Induced And Spontaneous Emission Without Resorting To Statistical Mechanics. -- Part I. Field Theory: 1. Microscopic Theory Of Radiation; 2. Lorentz Invariance And Second Quantization; 3. Classical Field Theory; 4. Old-fashioned Perturbation Theory; 5. Cross Sections And Decay Rates; 6. The S-matrix And Time-ordered Products; 7. Feynman Rules -- Part Ii. Quantum Electrodynamics: 8. Spin 1 And Gauge Invariance; 9. Scalar Quantum Electrodynamics; 10. Spinors; 11. Spinor Solutions And Cpt; 12. Spin And Statistics; 13. Quantum Electrodynamics; 14. Path Integrals -- Part Iii. Renormalization: 15. The Casimir Effect; 16. Vacuum Polarization; 17. The Anomalous Magnetic Moment; 18. Mass Renormalization; 19. Renormalized Perturbation Theory; 20. Infrared Divergences; 21. Renormalizability; 22. Non-renormalizable Theories; 23. The Renormalization Group; 24. Implications Of Unitarity -- Part Iv. The Standard Model: 25. Yang-mills Theory; 26. Quantum Yang-mills Theory; 27. Gluon Scattering And The Spinor-helicity Formalism; 28. Spontaneous Symmetry Breaking; 29. Weak Interactions; 30. Anomalies; 31. Precision Tests Of The Standard Model; 32. Quantum Chromodynamics And The Parton Model -- Part V. Advanced Topics: 33. Effective Actions And Schwinger Proper Time; 34. Background Fields; 35. Heavy-quark Physics; 36. Jets And Effective Field Theory -- Appendices. Matthew D. Schwartz, Harvard University. Includes Bibliographical References (pages 834-841) And Index. Quantum Field Theory And The Standard Model......Page 1 Half-Title......Page 3 Title-Page......Page 5 Copyright......Page 6 Dedication......Page 7 Contents......Page 9 Preface......Page 17 Part I Field theory......Page 21 1.1 Blackbody radiation......Page 23 1.2 Einstein coefficients......Page 25 1.3 Quantum field theory......Page 27 2.1 Lorentz invariance......Page 30 2.2 Classical plane waves as oscillators......Page 37 2.3 Second quantization......Page 40 Problems......Page 47 3.1 Hamiltonians and Lagrangians......Page 49 3.2 The Euler–Lagrange equations......Page 51 3.3 Noether's theorem......Page 52 3.4 Coulomb's law......Page 57 3.5 Green's functions......Page 59 Problems......Page 62 4 Old-fashioned perturbation theory......Page 66 4.1 Lippmann–Schwinger equation......Page 67 4.2 Early infinities......Page 72 Problems......Page 75 5 Cross sections and decay rates......Page 76 5.1 Cross sections......Page 77 5.2 Non-relativistic limit......Page 83 5.3 e[sup(+)]e[sup(-)]→μ[sup(+)]μ[sup(-)] with spin......Page 85 Problems......Page 87 6 The S-matrix and time-ordered products......Page 89 6.1 The LSZ reduction formula......Page 90 6.2 The Feynman propagator......Page 95 Problems......Page 97 7 Feynman rules......Page 98 7.1 Lagrangian derivation......Page 99 7.2 Hamiltonian derivation......Page 104 7.3 Momentum-space Feynman rules......Page 113 7.4 Examples......Page 117 7.A Normal ordering and Wick's theorem......Page 120 Problems......Page 123 Part II Quantum electrodynamics......Page 127 8.1 Unitary representations of the Poincaré group......Page 129 8.2 Embedding particles into fields......Page 133 8.3 Covariant derivatives......Page 140 8.4 Quantization and the Ward identity......Page 143 8.5 The photon propagator......Page 148 8.6 Is gauge invariance real?......Page 150 8.7 Higher-spin fields......Page 152 Problems......Page 158 9.1 Quantizing complex scalar fields......Page 160 9.2 Feynman rules for scalar QED......Page 162 9.3 Scattering in scalar QED......Page 166 9.4 Ward identity and gauge invariance......Page 167 9.5 Lorentz invariance and charge conservation......Page 170 Problems......Page 175 10 Spinors......Page 177 10.1 Representations of the Lorentz group......Page 178 10.2 Spinor representations......Page 183 10.3 Dirac matrices......Page 188 10.4 Coupling to the photon......Page 193 10.5 What does spin 1⁄2 mean?......Page 194 10.6 Majorana and Weyl fermions......Page 198 Problems......Page 201 11 Spinor solutions and CPT......Page 204 11.1 Chirality, helicity and spin......Page 205 11.2 Solving the Dirac equation......Page 208 11.3 Majorana spinors......Page 212 11.4 Charge conjugation......Page 213 11.5 Parity......Page 215 11.6 Time reversal......Page 218 Problems......Page 221 12 Spin and statistics......Page 225 12.1 Identical particles......Page 226 12.2 Spin-statistics from path dependence......Page 228 12.3 Quantizing spinors......Page 231 12.4 Lorentz invariance of the S-matrix......Page 232 12.5 Stability......Page 235 12.6 Causality......Page 239 Problems......Page 243 13 Quantum electrodynamics......Page 244 13.1 QED Feynman rules......Page 245 13.2 γ-matrix identities......Page 249 13.3 e[sup(+)]e[sup(-)]→-μ[sup(+)]μ[sup(-)]......Page 250 13.4 Rutherford scattering e[sup(-)]p[sup(+)]→e[sup(-)]p[sup(+)]......Page 254 13.5 Compton scattering......Page 258 13.6 Historical note......Page 266 Problems......Page 268 14.1 Introduction......Page 271 14.2 The path integral......Page 274 14.3 Generating functionals......Page 281 14.4 Where is the iε? ......Page 284 14.5 Gauge invariance......Page 287 14.6 Fermionic path integral......Page 289 14.7 Schwinger–Dyson equations......Page 292 14.8 Ward–Takahashi identity......Page 297 Problems......Page 303 Part III Renormalization......Page 305 15.1 Casimir effect......Page 307 15.2 Hard cutoff......Page 309 15.3 Regulator independence......Page 311 15.4 Scalar field theory example......Page 316 Problems......Page 319 16 Vacuum polarization......Page 320 16.1 Scalar ф[sup(3)] theory......Page 322 16.2 Vacuum polarization in QED......Page 324 16.3 Physics of vacuum polarization......Page 329 Problems......Page 334 17.1 Extracting the moment......Page 335 17.2 Evaluating the graphs......Page 338 Problems......Page 341 18 Mass renormalization......Page 342 18.1 Vacuum expectation values......Page 343 18.2 Electron self-energy......Page 344 18.3 Pole mass......Page 350 18.4 Minimal subtraction......Page 354 18.5 Summary and discussion......Page 356 Problems......Page 358 19.1 Counterterms......Page 359 19.2 Two-point functions......Page 362 19.3 Three-point functions......Page 365 19.4 Renormalization conditions in QED......Page 369 19.5 Z[sub(1)]=Z[sub(2)]: implications and proof......Page 370 Problems......Page 374 20 Infrared divergences......Page 375 20.1 e[sup(+)]e[sup(-)]→μ[sup(+)]μ[sup(-)] (+γ)......Page 376 20.2 Jets......Page 384 20.3 Other loops......Page 386 20.A Dimensional regularization......Page 393 Problems......Page 400 21 Renormalizability......Page 401 21.1 Renormalizability of QED......Page 402 21.2 Non-renormalizable field theories......Page 406 Problems......Page 413 22 Non-renormalizable theories......Page 414 22.1 The Schrödinger equation......Page 415 22.2 The 4-Fermi theory......Page 416 22.3 Theory of mesons......Page 420 22.4 Quantum gravity......Page 423 22.6 Mass terms and naturalness......Page 427 22.7 Super-renormalizable theories......Page 434 Problems......Page 436 23 The renormalization group......Page 437 23.1 Running couplings......Page 439 23.2 Renormalization group from counterterms......Page 443 23.3 Renormalization group equation for the 4-Fermi theory......Page 446 23.4 Renormalization group equation for general interactions......Page 449 23.5 Scalar masses and renormalization group flows......Page 455 23.6 Wilsonian renormalization group equation......Page 462 Problems......Page 470 24 Implications of unitarity......Page 472 24.1 The optical theorem......Page 473 24.2 Spectral decomposition......Page 486 24.3 Polology......Page 491 24.4 Locality......Page 495 Problems......Page 497 Part IV The Standard Model......Page 499 25 Yang–Mills theory......Page 501 25.1 Lie groups......Page 502 25.2 Gauge invariance and Wilson lines......Page 508 25.3 Conserved currents......Page 513 25.4 Gluon propagator......Page 515 25.5 Lattice gauge theories......Page 523 Problems......Page 526 26 Quantum Yang–Mills theory......Page 528 26.1 Feynman rules......Page 529 26.2 Attractive and repulsive potentials......Page 532 26.3 e[sup(+)]e[sup(-)]→hadrons and α[sub(s)]......Page 533 26.4 Vacuum polarization......Page 537 26.5 Renormalization at 1-loop......Page 541 26.6 Running coupling......Page 546 26.7 Defining the charge......Page 549 Problems......Page 553 27 Gluon scattering and the spinor-helicity formalism......Page 554 27.1 Spinor-helicity formalism......Page 555 27.2 Gluon scattering amplitudes......Page 562 27.3 gg→gg......Page 565 27.4 Color ordering......Page 568 27.5 Complex momenta......Page 571 27.6 On-shell recursion......Page 575 27.7 Outlook......Page 578 Problems......Page 579 28 Spontaneous symmetry breaking......Page 581 28.1 Spontaneous breaking of discrete symmetries......Page 582 28.2 Spontaneous breaking of continuous global symmetries......Page 583 28.3 The Higgs mechanism......Page 595 28.4 Quantization of spontaneously broken gauge theories......Page 600 Problems......Page 603 29.1 Electroweak symmetry breaking......Page 604 29.2 Unitarity and gauge boson scattering......Page 608 29.3 Fermion sector......Page 612 29.4 The 4-Fermi theory......Page 622 29.5 CP violation......Page 625 Problems......Page 634 30 Anomalies......Page 636 30.1 Pseudoscalars decaying to photons......Page 637 30.2 Triangle diagrams with massless fermions......Page 642 30.3 Chiral anomaly from the integral measure......Page 648 30.4 Gauge anomalies in the Standard Model......Page 651 30.5 Global anomalies in the Standard Model......Page 654 30.6 Anomaly matching......Page 658 Problems......Page 660 31 Precision tests of the Standard Model......Page 661 31.1 Electroweak precision tests......Page 662 31.2 Custodial SU(2), ρ, S, T and U......Page 673 31.3 Large logarithms in flavor physics......Page 677 Problems......Page 686 32 Quantum chromodynamics and the parton model......Page 687 32.1 Electron–proton scattering......Page 688 32.2 DGLAP equations......Page 697 32.3 Parton showers......Page 702 32.4 Factorization and the parton model from QCD......Page 705 32.5 Lightcone coordinates......Page 715 Problems......Page 718 Part V Advanced topics......Page 721 33 Effective actions and Schwinger proper time......Page 723 33.1 Effective actions from matching......Page 724 33.2 Effective actions from Schwinger proper time......Page 725 33.3 Effective actions from Feynman path integrals......Page 731 33.4 Euler–Heisenberg Lagrangian......Page 733 33.5 Coupling to other currents......Page 742 33.6 Semi-classical and non-relativistic limits......Page 745 33.A Schwinger's method......Page 748 Problems......Page 752 34 Background fields......Page 753 34.1 1PI effective action......Page 755 34.2 Background scalar fields......Page 763 34.3 Background gauge fields......Page 772 Problems......Page 778 35 Heavy-quark physics......Page 780 35.1 Heavy-meson decays......Page 782 35.2 Heavy-quark effective theory......Page 785 35.3 Loops in HQET......Page 788 35.4 Power corrections......Page 792 Problems......Page 795 36 Jets and effective field theory......Page 796 36.1 Event shapes......Page 798 36.2 Power counting......Page 800 36.3 Soft interactions......Page 802 36.4 Collinear interactions......Page 810 36.5 Soft-Collinear Effective Theory......Page 815 36.6 Thrust in SCET......Page 822 Problems......Page 830 Appendices......Page 833 A.1 Dimensional analysis......Page 835 A.2 Signs......Page 837 A.3 Feynman rules......Page 839 A.4 Dirac algebra......Page 840 Problems......Page 841 B.1 Integration parameters......Page 842 B.2 Wick rotations......Page 843 B.3 Dimensional regularization......Page 845 B.4 Other regularization schemes......Page 850 Problems......Page 853 References......Page 854 Index......Page 862 Minor corrections (Unimportant errors in equations)......Page 871 Typos (Superficial formatting issues)......Page 875 Important corrections (Errors in derivations or results)......Page 879 Minor corrections (Unimportant errors in equations)......Page 880 Typos (Superficial formatting issues)......Page 882 Minor corrections (Unimportant errors in equations)......Page 884 Typos (Superficial formatting issues)......Page 886 Back Cover......Page 892 Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of clear physical explanations, with direct connections to experimental data, and mathematical rigor make the subject accessible to students with a wide variety of backgrounds and interests. Assuming only an undergraduate-level understanding of quantum mechanics, the book steadily develops the Standard Model and state-of-the art calculation techniques. It includes multiple derivations of many important results, with modern methods such as effective field theory and the renormalization group playing a prominent role. Numerous worked examples and end-of-chapter problems enable students to reproduce classic results and to master quantum field theory as it is used today. Based on a course taught by the author over many years, this book is ideal for an introductory to advanced quantum field theory sequence or for independent study-- Résumé de l'éditeur Lorentz invariance and second quantization In the previous chapter, we saw that by treating each mode of electromagnetic radiation in a cavity a simple harmonic oscillator, we can derive Einstein's relation between the coefficients of induced and spontaneous emission without resorting to statistical mechanics. -- Résumé de l'éditeur