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E-raamat: Gauge Theories in Particle Physics: A Practical Introduction, Volume 1: From Relativistic Quantum Mechanics to QED, Fourth Edition

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(Microsoft Research), (Professor Emeritus, University of Oxford, UK, and Visiting Scientist, SLAC National Accelerator Laboratory, California, USA)
  • Formaat: 438 pages
  • Ilmumisaeg: 17-Dec-2012
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781466513020
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Gauge Theories in Particle Physics: A Practical Introduction, Volume 1: From Relativistic Quantum Mechanics to QED, Fourth EditionSuurem pilt
  • Formaat: 438 pages
  • Ilmumisaeg: 17-Dec-2012
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781466513020
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Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).

The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a unique elementary introduction to quantum field theory, establishing the essentials of the formal and conceptual framework upon which the subsequent development of the three gauge theories is based. The text also describes tree-level calculations of physical processes in QED and introduces ideas of renormalization in the context of one-loop radiative corrections for QED.

New to the Fourth Edition

  • New chapter on Lorentz transformations and discrete symmetries in relativistic quantum mechanics, with physical applications
  • Introduction of Majorana fermions at an early stage, making the material suitable for a first course in relativistic quantum mechanics
  • Discrete symmetries in quantum field theory
  • Updates on nucleon structure functions and the status of QED

The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight.

Arvustused

"Aitchison and Hey was the bible for me as a young post-doc in the 1980s The book has been revised regularly as the field progressed and I am delighted to see a new edition which brings it up to date to the discovery of a Higgs-like boson at the LHC in July 2012. As an experimentalist, this book helped me understand the theoretical underpinnings of my work. Its strength has always been the combination of the theory with discussion of experimental results. The new edition continues this tradition by including background on discrete symmetries This will become a new classic." Amanda Cooper-Sarkar, Oxford University, UK

"This is an indispensable textbook for all particle physicists, experimentalists and theorists alike, providing an accessible exposé of the Standard Model, covering the mathematics used to describe it and some of the most important experimental results which vindicate it. As a lecturer in an advanced course on the Standard Model for experimentalists, I use the books for the more theoretical aspects and as a constant source for clear explanations of the underlying physics. I also know it to be the recommended text on numerous theoretical modules in particle physics. these textbooks will remain on the top of a high energy physicists reading list for years to come." Matthew Wing, University College London, UK

Preface xiii
I Introductory Survey, Electromagnetism as a Gauge Theory, and Relativistic Quantum Mechanics
1(112)
1 The Particles and Forces of the Standard Model
3(38)
1.1 Introduction: the Standard Model
3(1)
1.2 The fermions of the Standard Model
4(8)
1.2.1 Leptons
4(4)
1.2.2 Quarks
8(4)
1.3 Particle interactions in the Standard Model
12(18)
1.3.1 Classical and quantum fields
12(3)
1.3.2 The Yukawa theory of force as virtual quantum exchange
15(4)
1.3.3 The one-quantum exchange amplitude
19(2)
1.3.4 Electromagnetic interactions
21(1)
1.3.5 Weak interactions
22(4)
1.3.6 Strong interactions
26(3)
1.3.7 The gauge bosons of the Standard Model
29(1)
1.4 Renormalization and the Higgs sector of the Standard Model
30(4)
1.4.1 Renormalization
30(3)
1.4.2 The Higgs boson of the Standard Model
33(1)
1.5 Summary
34(7)
Problems
35(6)
2 Electromagnetism as a Gauge Theory
41(22)
2.1 Introduction
41(2)
2.2 The Maxwell equations: current conservation
43(2)
2.3 The Maxwell equations: Lorentz covariance and gauge invariance
45(4)
2.4 Gauge invariance (and covariance) in quantum mechanics
49(3)
2.5 The argument reversed: the gauge principle
52(4)
2.6 Comments on the gauge principle in electromagnetism
56(7)
Problems
62(1)
3 Relativistic Quantum Mechanics
63(24)
3.1 The Klein-Gordon equation
63(3)
3.1.1 Solutions in coordinate space
64(1)
3.1.2 Probability current for the KG equation
65(1)
3.2 The Dirac equation
66(6)
3.2.1 Free-particle solutions
69(1)
3.2.2 Probability current for the Dirac equation
70(2)
3.3 Spin
72(2)
3.4 The negative-energy solutions
74(6)
3.4.1 Positive-energy spinors
74(1)
3.4.2 Negative-energy spinors
75(1)
3.4.3 Dirac's interpretation of the negative-energy solutions of the Dirac equation
76(1)
3.4.4 Feynman's interpretation of the negative-energy solutions of the KG and Dirac equations
77(3)
3.5 Inclusion of electromagnetic interactions via the gauge principle: the Dirac prediction of g = 2 for the electron
80(7)
Problems
83(4)
4 Lorentz Transformations and Discrete Symmetries
87(26)
4.1 Lorentz transformations
87(8)
4.1.1 The KG equation
87(2)
4.1.2 The Dirac equation
89(6)
4.2 Discrete transformations: P, C and T
95(18)
4.2.1 Parity
95(4)
4.2.2 Charge conjugation
99(4)
4.2.3 CP
103(1)
4.2.4 Time reversal
104(4)
4.2.5 CPT
108(1)
Problems
109(4)
II Introduction to Quantum Field Theory
113(106)
5 Quantum Field Theory I: The Free Scalar Field
115(34)
5.1 The quantum field: (i) descriptive
115(10)
5.2 The quantum field: (ii) Lagrange-Hamilton formulation
125(19)
5.2.1 The action principle: Lagrangian particle mechanics
125(4)
5.2.2 Quantum particle mechanics a la Heisenberg-Lagrange-Hamilton
129(2)
5.2.3 Interlude: the quantum oscillator
131(2)
5.2.4 Lagrange-Hamilton classical field mechanics
133(4)
5.2.5 Heisenberg-Lagrange-Hamilton quantum field mechanics
137(7)
5.3 Generalizations: four dimensions, relativity and mass
144(5)
Problems
146(3)
6 Quantum Field Theory II: Interacting Scalar Fields
149(34)
6.1 Interactions in quantum field theory: qualitative introduction
149(3)
6.2 Perturbation theory for interacting fields: the Dyson expansion of the S-matrix
152(6)
6.2.1 The interaction picture
153(3)
6.2.2 The S-matrix and the Dyson expansion
156(2)
6.3 Applications to the 'ABC theory
158(25)
6.3.1 The decay C → A + B
159(4)
6.3.2 A + B → A + B scattering: the amplitudes
163(9)
6.3.3 A + B → A + B scattering: the Yukawa exchange mechanism, s and u channel processes
172(2)
6.3.4 A + B → A + B scattering: the differential cross section
174(3)
6.3.5 A + B → A + B scattering: loose ends
177(2)
Problems
179(4)
7 Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields; Introduction of Electromagnetic Interactions
183(36)
7.1 The complex scalar field: global U(1) phase invariance, particles and antiparticles
184(7)
7.2 The Dirac field and the spin-statistics connection
191(5)
7.3 The Maxwell field Aμ(x)
196(10)
7.3.1 The classical field case
196(3)
7.3.2 Quantizing Aμ(x)
199(7)
7.4 Introduction of electromagnetic interactions
206(4)
7.5 P, C and T in quantum field theory
210(9)
7.5.1 Parity
210(1)
7.5.2 Charge conjugation
211(2)
7.5.3 Time reversal
213(2)
Problems
215(4)
III Tree-Level Applications in QED
219(78)
8 Elementary Processes in Scalar and Spinor Electrodynamics
221(48)
8.1 Coulomb scattering of charged spin-0 particles
221(6)
8.1.1 Coulomb scattering of s+ (wavefunction approach)
221(3)
8.1.2 Coulomb scattering of s+ (field-theoretic approach)
224(1)
8.1.3 Coulomb scattering of s-
225(2)
8.2 Coulomb scattering of charged spin-1/2 particles
227(7)
8.2.1 Coulomb scattering of e- (wavefunction approach)
227(3)
8.2.2 Coulomb scattering of e- (field-theoretic approach)
230(1)
8.2.3 Trace techniques for spin summations
230(3)
8.2.4 Coulomb scattering of e+
233(1)
8.3 e-s+ scattering
234(8)
8.3.1 The amplitude for e-s+ → e-s+
234(5)
8.3.2 The cross section for e-s+ → e-s+
239(3)
8.4 Scattering from a non-point-like object: the pion form factor in e-π+ → e-π+
242(5)
8.4.1 e- scattering from a charge distribution
243(1)
8.4.2 Lorentz invariance
244(1)
8.4.3 Current conservation
245(2)
8.5 The form factor in the time-like region: e+e- → π+π- and crossing symmetry
247(3)
8.6 Electron Compton scattering
250(4)
8.6.1 The lowest-order amplitudes
250(1)
8.6.2 Gauge invariance
251(1)
8.6.3 The Compton cross section
252(2)
8.7 Electron muon elastic scattering
254(3)
8.8 Electron-proton elastic scattering and nucleon form factors
257(12)
8.8.1 Lorentz invariance
258(1)
8.8.2 Current conservation
259(4)
Problems
263(6)
9 Deep Inelastic Electron-Nucleon Scattering and the Parton Model
269(28)
9.1 Inelastic electron-proton scattering: kinematics and structure functions
269(3)
9.2 Bjorken scaling and the parton model
272(9)
9.3 Partons as quarks and gluons
281(3)
9.4 The Drell-Yan process
284(4)
9.5 e+e- annihilation into hadrons
288(9)
Problems
292(5)
IV Loops and Renormalization
297(64)
10 Loops and Renormalization I: The ABC Theory
299(28)
10.1 The propagator correction in ABC theory
300(11)
10.1.1 The O(g2) self-energy Π[ 2](q2)
300(7)
10.1.2 Mass shift
307(1)
10.1.3 Field strength renormalization
308(3)
10.2 The vertex correction
311(3)
10.3 Dealing with the bad news: a simple example
314(4)
10.3.1 Evaluating Π[ 2](q2)
314(2)
10.3.2 Regularization and renormalization
316(2)
10.4 Bare and renormalized perturbation theory
318(6)
10.4.1 Reorganizing perturbation theory
318(3)
10.4.2 The O(g2ph) renormalized self-energy revisited: how counter terms are determined by renormalization conditions
321(3)
10.5 Renormalizability
324(3)
Problems
326(1)
11 Loops and Renormalization II: QED
327(34)
11.1 Counter terms
327(2)
11.2 The O(e2) fermion self-energy
329(2)
11.3 The O(e2) photon self-energy
331(2)
11.4 The O(e2) renormalized photon self-energy
333(3)
11.5 The physics of Π[ 2]y(q2)
336(9)
11.5.1 Modified Coulomb's law
336(2)
11.5.2 Radiatively induced charge form factor
338(1)
11.5.3 The running coupling constant
339(5)
11.5.4 Πy[ 2] in the s-channel
344(1)
11.6 The O(e2) vertex correction, and Z1 = Z2
345(3)
11.7 The anomalous magnetic moment and tests of QED
348(5)
11.8 Which theories are renormalizable - and does it matter?
353(8)
Problems
360(1)
A Non-relativistic Quantum Mechanics
361(4)
B Natural Units
365(4)
C Maxwell's Equations: Choice of Units
369(2)
D Special Relativity: Invariance and Covariance
371(6)
E Dirac δ-Function
377(10)
F Contour Integration
387(6)
G Green Functions
393(6)
H Elements of Non-relativistic Scattering Theory
399(6)
H.1 Time-independent formulation and differential cross section
399(2)
H.2 Expression for the scattering amplitude: Born approximation
401(1)
H.3 Time-dependent approach
402(3)
I The Schrodinger and Heisenberg Pictures
405(2)
J Dirac Algebra and Trace Identities
407(4)
J.1 Dirac algebra
407(2)
J.1.1 y matrices
407(1)
J.1.2 y5 identities
407(1)
J.1.3 Hermitian conjugate of spinor matrix elements
408(1)
J.1.4 Spin sums and projection operators
408(1)
J.2 Trace theorems
409(2)
K Example of a Cross Section Calculation
411(6)
K.1 The spin-averaged squared matrix element
413(1)
K.2 Evaluation of two-body Lorentz-invariant phase space in `laboratory' variables
413(4)
L Feynman Rules for Tree Graphs in QED
417(4)
L.1 External particles
417(1)
L.2 Propagators
418(1)
L.3 Vertices
418(3)
References 421(6)
Index 427
Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford and a visiting scientist at SLAC National Accelerator Laboratory. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of Relativistic Quantum Mechanics, An Informal Introduction to Gauge Field Theories, and Supersymmetry in Particle Physics and joint editor of two other books.

Anthony J.G. Hey is Vice President of Microsoft Research Connections, where he is responsible for the worldwide external research and technical computing strategy across Microsoft Corporation. A fellow of the U.K. Royal Academy of Engineering, Dr. Hey was previously the director of the U.K. e-Science Initiative and the head of the School of Electronics and Computer Science and dean of Engineering and Applied Science at the University of Southampton. His research interests encompass parallel programming for parallel systems built from mainstream commodity components. With Jack Dongarra, Rolf Hempel, and David Walker, he wrote the first draft of a specification for a new message-passing standard called MPI. This initiated the process that led to the successful MPI standard of today.
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