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Introduction to Gauge Theories [Kõva köide]

(University of Rome, La Sapienza, and INFN Rome, Italy), (INFN, Roma, Italy), (University of Rome, La Sapienza, Italy, and Istituto Nazionale di Fisica Nucleare, Roma, Italy)
  • Formaat: Hardback, 320 pages, kõrgus x laius: 234x156 mm, kaal: 580 g, 47 Line drawings, black and white; 5 Halftones, black and white; 52 Illustrations, black and white
  • Ilmumisaeg: 11-Jul-2017
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498734510
  • ISBN-13: 9781498734516
  • Formaat: Hardback, 320 pages, kõrgus x laius: 234x156 mm, kaal: 580 g, 47 Line drawings, black and white; 5 Halftones, black and white; 52 Illustrations, black and white
  • Ilmumisaeg: 11-Jul-2017
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498734510
  • ISBN-13: 9781498734516
Written by world-leading experts in particle physics, this new book from Luciano Maiani and Omar Benhar, with contributions from the late Nicola Cabibbo, is based on Feynmans path integrals. Key elements of gauge theories are describedFeynman diagrams, gauge-fixing, Faddeev-Popov ghostsas well as renormalization in Quantum Electrodynamics. Quarks and QCD interactions are introduced. Renormalization group and high momentum behaviour of the coupling constants is discussed in QED and QCD, with asymptotic freedom derived at one-loop. These concepts are related to the Higgs boson and models of grand unification.

" an excellent introduction to the quantum theory of gauge fields and their applications to particle physics. It will be an excellent book for the serious student and a good reference for the professional practitioner. Let me add that, scattered through the pages, we can find occasional traces of Nicola Cabibbo's style." John Iliopoulos, CNRS-Ecole Normale Supérieure

" The volume ends with an illuminating description of the expectation generated by the recent discovery of the Higgs boson, combined with the lack of evidence for super-symmetric particles in the mass range 0.6-1 TeV." Arturo Menchaca-Rocha, FinstP, Professor of Physics, Mexicos National Autonomous University, Former President of the Mexican Academy of Sciences, Presidential Advisor

"The reader is masterfully guided through the subtleties of the quantum field theory and elementary particle physics from simple examples in Quantum Mechanics to salient details of modern theory." Mikhail Voloshin, Professor of Physics, University of Minnesota

Arvustused

"This book on gauge theories completes a trilogy on the foundations of the Standard Theory of the fundamental interactions, but is fully self-contained. It combines the depth and conceptual accuracy expected from key contributors to the field with an effective pedagogical approach, tested over several decades of courses. The mathematical formalism is never overwhelming, and the reader is guided through the concepts and techniques of quantum gauge theories along a path always driven by physics, including recent developments on the Higgs boson. This book is a great legacy of the `Rome School for students, teachers and researchers in particle physics, not only theorists but also curious experimentalists." Fabio Zwirner, University of Padua

"Introduction to Gauge Theories is authored by leading contributors to the Standard Model of Particle Physic (SM): Nicola Cabibbo (the proponent of quark mixing angles, whose extension led to the Cabibbo-Kobayashi-Maskawa matrix); Luciano Maiani (one of the fathers of the so-called GIM mechanism which led to the prediction of the quark charm); and Omar Benhar (a well-known expert in many-body physics) and it constitutes a most welcome addition to the literature. A must-have in any physics library, this book is highly original, centring on deep problems of quantum field theory, and consistently well-motivated by experimental phenomena. The symmetries of nature are the guiding principle, illuminating the presentation of the concept of renormalisation and its applications in gauge theories, from a thorough and pedagogical analysis of Quantum Electrodynamics, to the exploration of Quantum Chromodynamics and the SM, including the role of the Higgs field, and beyond. Everybody can find some food for thought here: from the graduate student to the most hardened researcher. This book is full of physical insights and is highly recommended." Belén Gavela, Professor of Theoretical Physics at

List of Figures
xi
Preface xiii
The Authors xv
Chapter 1 Introduction
1(4)
1.1 Quantum Electrodynamics
1(2)
1.2 Units and Other Conventions
3(2)
Chapter 2 The Feynman Path Integral
5(12)
2.1 Calculation of the Transition Amplitude
5(3)
2.2 The Lattice Approximation
8(1)
2.3 The Classical Limit
9(1)
2.4 Time As A Complex Variable
9(2)
2.5 Statistical Mechanics
11(1)
2.6 Green's Functions
12(5)
Chapter 3 Towards A Field Theory
17(20)
3.1 The Generating Functional
20(3)
3.2 The Harmonic Oscillator
23(5)
3.3 Free Scalar Fields: Propagator and Generating Functional
28(3)
3.4 Free Scalar Field: One-Particle States
31(2)
3.5 Creation and Destruction Operators
33(4)
Chapter 4 Equations of Motion, Symmetries and Ward's Identity
37(18)
4.1 Sum Over Paths and Operators
38(1)
4.1.1 Derivatives
39(1)
4.2 The Fundamental Identity
39(2)
4.3 Quantum Mechanics
41(5)
4.3.1 Equations of motion and commutation rules
41(2)
4.3.2 Symmetries
43(2)
4.3.3 The Hamiltonian function
45(1)
4.4 Field Theory
46(6)
4.4.1 Symmetries in field theory
47(2)
4.4.2 Ward's identity
49(3)
4.5 The Symmetries of The Vacuum
52(3)
Chapter 5 The Electromagnetic Field
55(12)
5.1 The Choice of Gauge
56(2)
5.2 Generating Functional and Propagator
58(1)
5.3 Single Photon States
59(3)
5.4 Virtual Photons
62(5)
Chapter 6 Fermion Fields
67(18)
6.1 Harmonic and Fermi Oscillators
67(9)
6.1.1 Anticommuting variables
69(1)
6.1.2 Sum over paths for the two oscillators
70(4)
6.1.3 Gaussian integrals for commuting and anticommuting variables
74(2)
6.2 Quantisation of the Dirac Field
76(9)
6.2.1 Fermion propagator
79(1)
6.2.2 The spin-statistics theorem
79(2)
6.2.3 One-particle states of the Dirac field
81(4)
Chapter 7 Scattering Processes and the S-Matrix
85(14)
7.1 "In" States and "Out" States
86(3)
7.2 Scattering Amplitudes and the S-Matrix
89(1)
7.3 Conserved Quantities
90(1)
7.4 The Lsz Reduction Formulae
91(8)
Chapter 8 Perturbative Green's Functions in λφ4
99(18)
8.1 The Perturbative Generating Functional
100(4)
8.2 Feynman Rules for Green's Functions
104(6)
8.3 Connected Parts and Vacuum Diagrams
110(2)
8.4 PERTURBATIVE TWO-POINT GREEN'S FUNCTION
112(5)
Chapter 9 S-Matrix Feynman Diagrams in λφ4
117(6)
9.1 One-Particle Irreducible Diagrams
117(3)
9.2 Feynman Rules for the S-Matrix Elements
120(3)
Chapter 10 Quantum Electrodynamics
123(16)
10.1 Feynman Diagrams for the Generating Functional
125(3)
10.2 Two-Point Functions
128(2)
10.3 Reduction Formulae
130(2)
10.4 Feynman Diagrams for the S-Matrix
132(4)
10.5 Combinatorials
136(3)
Chapter 11 Renormalisation of Qed
139(16)
11.1 The Photon Propagator
142(3)
11.2 Renormalisation of the Charge
145(1)
11.3 The Electron Propagator
146(5)
11.3.1 The propagator to all orders
149(2)
11.4 The Vertex
151(2)
11.5 Ward's Identity
153(2)
Chapter 12 Applications of Qed
155(20)
12.1 Scattering In An External Field
155(3)
12.2 Bremsstrahlung and Infrared Divergence
158(4)
12.3 The Lamb Shift
162(4)
12.4 Vacuum Polarisation
166(3)
12.4.1 Calculation of the tensor Πμν(k) to one loop
166(3)
12.5 The Anomalous Magnetic Moment
169(6)
12.5.1 Preliminaries
169(2)
12.5.2 The calculation
171(4)
Chapter 13 Renormalisation Group of Qed
175(8)
13.1 Effective Electric Charge
176(3)
13.2 The Gell-Mann and Low Equation
179(1)
13.3 The Qed β Function
180(1)
13.4 Asymptotic Variation of the Effective Charge
181(2)
Chapter 14 Quantising A Non-Abelian Theory
183(12)
14.1 Fundamentals
183(3)
14.2 Quarks In Quantum Chromodynamics
186(2)
14.3 The Faddeev-Popov Determinant
188(4)
14.4 Feynman Rules
192(3)
Chapter 15 The β Function In Qcd
195(10)
15.1 Vacuum Polarisation
195(5)
15.2 Corrections To Quark Propagator and Vertex
200(2)
15.3 Asymptotic Freedom
202(3)
Chapter 16 Unitarity and Ghosts
205(12)
16.1 The Cutkosky Rule
206(1)
16.2 The Inelastic Reaction u + u → d + d
207(3)
16.3 The Case of Qed
210(2)
16.4 Non-Abelian Gauge Theories
212(5)
Chapter 17 Effective Constants At High Energy and Grand Unification
217(12)
17.1 The Determination Of αs
217(1)
17.2 The Landau Pole and the Continuum Limit
218(2)
17.3 Effective Constants of the Standard Theory
220(4)
17.4 Grand Unification and Other Hypotheses
224(5)
Chapter 18 Limits on the Mass of the Higgs Boson
229(10)
18.1 Scalar Fields In the Standard Theory
229(5)
18.2 Limits On the Mass of the Higgs Boson
234(5)
Chapter 19 The Weak Muon Anomaly
239(12)
19.1 The Rξ Gauge
240(4)
19.2 Muon Anomaly: W Exchange
244(3)
19.3 Z and Higgs Boson Exchange
247(1)
19.4 Comparison With Data
248(3)
Chapter 20 Effective Potential and Naturalness
251(18)
20.1 Effective Potential
251(2)
20.2 Expansion Around the Classical Limit
253(4)
20.3 Loop Expansion of the Potential
257(1)
20.4 One Loop Potential in the Standard Theory
258(6)
20.5 Non-Naturalness of the Standard Theory
264(5)
Appendix A Transition Amplitude Calculation
269(2)
A.1 Transition Amplitude for Zero Potential
269(2)
Appendix B Connected Diagrams
271(4)
B.1 Generating Functional of Connected Diagrams
271(4)
Appendix C Lorentz invariance and one-particle states
275(4)
C.1 Renormalisation Constants
275(4)
Appendix D Reduction formulae
279(4)
D.1 Reduction Formulae for the Compton Scattering Amplitude
279(4)
Appendix E Integrals
283(4)
E.1 Integration In D Dimensions
283(2)
E.2 Feynman Parameters
285(2)
Appendix F β(λ) and β(gt) functions
287(8)
F.1 Calculation of the β(λ) and β(gt) Functions
287(1)
F.2 β(λ)
287(6)
F.3 β(gt)
293(2)
Bibliography 295(4)
Index 299
Nicola Cabibbo (1935-2010) was professor of Theoretical Physics and Elementary Particle Phyiscs at the Rome Universities La Sapienza and Tor Vergata, and held research and teaching positions in prestigious institutions such as Harvard University, the Institute for Advanced Studies, Princeton, CERN, Geneva, University of California at Berkeley and Universite Paris VI. In 1962, Cabibbo discovered the phenomenon of quark mixing, described by a new natural constant, the Cabibbo angle, measured with great accuracy in semileptonic weak decays of hadrons. According to a recent analysis, Cabibbo's paper on quark mixing was the most influential article published in the journals of the American Physical Society during 1893-2003. In the 1980s, Cabibbo provided important momentum to the applications of numerical techniques to theoretical physics, notably the gauge theories of strong interactions, promoting and leading the development of the family of APE (Array Processor Experiment) supercomputers. He served as a member of a number of learned societies: Accademia Nazionale dei Lincei and Accademia delle Scienze di Torino, in Italy, National Academy of Science and American Association for Art and Sciences, in the USA, and Accademia Pontificia delle Scienze, which he chaired from 1993. An internationally reputed science manager, Cabibbo was President of Istituto Nazionale di Fisica Nucleare (INFN) and of Ente Nazionale per le Nuove Tecnologie per Energia e Ambiente (ENEA). He was the recipient of the J.J. Sakurai Prize (APS), the Medaglia Matteucci (Accademia Nazionale dei XL), the Dirac Medal, (ICTP Trieste), and the Benjamin Franklin Medal.

Luciano Maiani is emeritus professor of theoretical physics at the University of Rome, "La Sapienza", and author of more than two hundred scientic publications on the theoretical physics of elementary particles. Together with S. Glashow and J. Iliopoulos, Maiani made the prediction of a new family of particles, those with "charm", which form an essential part of the unifed theory of the weak and electromagnetic forces. He has been president of the Italian Institute for Nuclear Physics (INFN), director-general of CERN in Geneva and president of the Italian National Council for Research (CNR). Has promoted the development of the Virgo Observatory for gravitational wave detection, the neutrino beam from CERN to Gran Sasso and at CERN has directed the crucial phases of the construction of the Large Hadron Collider (LHC). He has taught and worked in numerous foreign institutes. He was head of the theoretical physics department at the University of Rome, "La Sapienza", from 1976 to 1984 and held the chair of theoretical physics from 1984 to 2011. He is a member of the Italian Lincean Academy and a fellow of the American Physical Society. For his scientific work, he has been awarded the J. J. Sakurai Prize, the Enrico Fermi Prize, the Dirac Medal, the High Energy and Particle Physics Prize of EPS and the Bruno Pontecorvo Prize.

Omar Benhar is an INFN research director and teaches gauge theories at the University of Rome, "La Sapienza". He has worked extensively in the United States as a visiting professor, at the University of Illinois and Old Dominion University, and was an associate scientist at the Thomas Jeerson National Accelerator Facility. Since 2013, he has served as an adjunct professor at the Centre for Neutrino Physics of Virginia Polytechnic Institute and State University. He is the author of more than a hundred scientific papers on the theory of many-particle systems, the structure of compact stars and electroweak interactions of nuclei.