Gauge Theories in Particle Physics: Volume I: From Relativistic Quantum Mechanics to QED, Third Edition

Copertina anteriore
CRC Press, 1 set 2002 - 422 pagine
Gauge Theories in Particle Physics, Volume 1: From Relativistic Quantum Mechanics to QED, Third Edition presents an accessible, practical, and comprehensive introduction to the three gauge theories of the standard model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the electroweak theory. For each of them, the authors provide a thorough discussion of the main conceptual points, a detailed exposition of many practical calculations of physical quantities, and a comparison of these quantitative predictions with experimental results.

For this two-volume third edition, much of the book has been rewritten to reflect developments over the last decade, both in the curricula of university courses and in particle physics research. Substantial new material has been introduced that is intended for use in undergraduate physics courses. New introductory chapters provide a precise historical account of the properties of quarks and leptons, and a qualitative overview of the quantum field description of their interactions, at a level appropriate to third year courses. The chapter on relativistic quantum mechanics has been enlarged and is supplemented by additional sections on scattering theory and Green functions, in a form appropriate to fourth year courses. Since precision experiments now test the theories beyond lowest order in perturbation theory, an understanding of the data requires a more sophisticated knowledge of quantum field theory, including ideas of renormalization. The treatment of quantum field theory has therefore been considerably extended so as to provide a uniquely accessible and self-contained introduction to quantum field dynamics, as described by Feynman graphs. The level is suitable for advanced fourth year undergraduates and first year graduates.

These developments are all contained in the first volume, which ends with a discussion of higher order corrections in QED; the second volume is devoted to the non-Abelian gauge theories of QCD and the electroweak theory. As in the first two editions, emphasis is placed throughout on developing realistic calculations from a secure physical and conceptual basis.
 

Sommario

QUARKS AND LEPTONS
3
from atoms to quarks
5
122 Nuclei nucleons
8
123 Nucleons quarks
12
13 The generations and flavours of quarks and leptons
18
132 Quark flavour
21
PARTICLE INTERACTIONS IN THE STANDARD MODEL
28
22 The Yukawa theory of force as virtual quantum exchange
30
822 Coulomb scattering of e fieldtheoretic approach
213
823 Trace techniques for spin summations
214
824 Coulomb scattering of e+
217
83 es+ scattering
218
832 The cross section for es+ es+
223
the pion form factor in
225
842 Lorentz invariance
227
843 Current conservation
228

23 The onequantum exchange amplitude
34
24 Electromagnetic interactions
35
25 Weak interactions
37
26 Strong interactions
40
27 Gravitational interactions
44
28 Summary
48
Problems
49
ELECTROMAGNETISM AS A GAUGE THEORY
53
current conservation
54
Lorentz covariance and gauge invariance
56
34 Gauge invariance and covariance in quantum mechanics
60
the gauge principle
63
36 Comments on the gauge principle in electromagnetism
67
Problems
73
RELATIVISTIC QUANTUM MECHANICS
74
411 Solutions in coordinate space
75
412 Probability current for the KG equation
76
42 The Dirac equation
77
421 Freeparticle solutions
80
422 Probability current for the Dirac equation
81
43 Spin
82
44 Lorentz transformation properties of spinors
85
45 The negativeenergy solutions
91
451 Positiveenergy spinors
92
453 Diracs interpretation of the negativeenergy solutions of the Dirac equation
93
454 Feynmans interpretation of the negativeenergy solutions of the KG and Dirac equations
95
the Dirac prediction of g 2 for the electron
98
Problems
101
QUANTUM FIELD THEORY I THE FREE SCALAR FIELD
109
ii LagrangeHamilton formulation
119
522 Quantum mechanics à la HeisenbergLagrangeHamilton
122
the quantum oscillator
124
524 LagrangeHamilton classical field mechanics
127
525 HeisenbergLagrangeHamilton quantum field mechanics
129
four dimensions relativity and mass
136
Problems
139
QUANTUM FIELD THEORY II INTERACTING SCALAR FIELDS
141
the Dyson expansion of the Smatrix
144
621 The interaction picture
145
622 The Smatrix and the Dyson expansion
147
63 Applications to the ABC theory
150
631 The decay C A + B
151
the amplitudes
155
the Yukawa exchange mechanism s and u channel processes
164
the differential cross section
166
loose ends
168
Problems
171
QUANTUM FIELD THEORY III COMPLEX SCALAR FIELDS DIRAC AND MAXWELL FIELDS INTRODUCTION OF ELECTROMAGNETIC I...
173
global UI phase invariance particles and antiparticles
174
72 The Dirac field and the spinstatistics connection
181
731 The classical field case
186
732 Quantizing A𝝁x
189
74 Introduction of electromagnetic interactions
195
Problems
200
ELEMENTARY PROCESSES IN SCALAR AND SPINOR ELECTRODYNAMICS
205
812 Coulomb scattering of s+ fieldtheoretic approach
208
813 Coulomb scattering of s
209
82 Coulomb scattering of charged spin½ particles
210
e+e 𝞹+𝞹 and crossing symmetry
230
86 Electron Compton scattering
233
862 Gauge invariance
234
863 The Compton cross section
235
87 Electron muon elastic scattering
237
88 Electronproton elastic scattering and nucleon form factors
240
881 Lorentz invariance
241
Problems
244
DEEP INELASTIC ELECTRONNUCLEON SCATTERING AND THE QUARK PARTON MODEL
249
92 Bjorken scaling and the parton model
252
93 The quark parton model
260
94 The DrellYan process
262
e+e annihilation into hadrons
267
Problems
272
LOOPS AND RENORMALIZATION I THE ABC THEORY
279
101 The propagator correction in ABC theory
280
1012 Mass shift
287
1013 Field strength renormalization
288
102 The vertex correction
291
a simple example
293
1032 Regularization and renormalization
296
104 Bare and renormalized perturbation theory
297
how counter terms are determined by renormalization conditions
300
105 Renormalizability
303
Problems
304
LOOPS AND RENORMALIZATION II QED
306
112 The Oe² fermion selfenergy
308
113 The Oe² photon selfenergy
309
1 14 The Oe² renormalized photon selfenergy
312
115 The physics of 𝞹y2q²
314
1151 Modified Coulombs law
315
1152 Radiatively induced charge form factor
317
1 154 𝞹y2 in the schannel
322
1 16 The Oe² vertex correction and Z₁ Z₂
323
117 The anomalous magnetic moment and tests of QED
326
118 Which theories are renormalizableand does it matter?
329
Problems
336
Nonrelativistic Quantum Mechanics
338
Natural Units
342
Maxwells Equations Choice of Units
345
Special Relativity Invariance and Covariance
347
Dirac 𝛿5Function
352
Contour Integration
360
Green Functions
366
Elements of Nonrelativistic Scattering Theory
372
Born approximation
374
H3 Timedependent approach
375
The Schrödinger and Heisenberg Pictures
377
Dirac Algebra and Trace Identities
379
J13 Hermitian conjugate of spinor matrix elements
380
J2 Trace theorems
381
Example of a Cross Section Calculation
383
K1 The spinaveraged squared matrix element
385
Feynman Rules for Tree Graphs in QED
389
L2 Propagators
390
References
391
Index
395
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