Gauge Theory of Elementary Particle Physics Problems and Solutions

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Format: Paperback
Pub. Date: 2000-05-04
Publisher(s): Oxford University Press
List Price: $114.11

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Summary

Students of particle physics often find it difficult to locate resources to learn calculational techniques as intermediate steps are usually not given in the research literature. To a certain extent, this is the case even in some of the established textbooks. In this book of worked problems enough details are provided so that the beginner will understand the solution in each particular case. With this step-by-step guidance, students (after first attempting the solution themselves) can develop their skills and confidence in their ability to work out particle theory problems. Besides being a problems/solutions addition to the well established textbook by Cheng & Li, this book introduces several new topics. It provides the reader with a self-contained approach to the subject, suitable even for those not familiar with the textbook. All problems have been given a descriptive title, enabling the reader to select according to his preferences.

Table of Contents

Field quantization
Simple exercises in λø4 theory
1(5)
Auxiliary field
6(2)
Disconnected diagrams
8(1)
Simple external field problem
9(2)
Path integral for a free particle
11(2)
Path integral for a general quadratic action
13(3)
Spreading of a wave packet
16(1)
Path integral for a harmonic oscillator
17(4)
Path integral for a partition function
21(2)
Partition function for an SHO system
23(2)
Non-standard path-integral representation
25(1)
Weyl ordering of operators
26(6)
Generating functional for a scalar field
32(3)
Poles in Green's function
35(2)
Renormalization
Counterterms in λø4 theory and in QED
37(2)
Divergences in non-linear chiral theory
39(2)
Divergences in lower-dimensional field theories
41(2)
n-Dimensional `spherical' coordinates
43(3)
Some integrals in dimensional regularization
46(3)
Vacuum polarization and subtraction schemes
49(4)
Renormalization of λø3 theory in n dimensions
53(4)
Renormalization of composite operators
57(2)
Cutkosky rules
59(4)
Renormalization group
Homogeneous renormalization-group equation
63(1)
Renormalization constants
64(3)
β-function for QED
67(2)
Behaviour of g near a simple fixed point
69(1)
Running coupling near a general fixed point
70(1)
One-loop renormalization-group equation in massless λø4 theory
71(1)
β-function for the Yukawa coupling
72(3)
Solving the renormalization-group equation by Coleman's method
75(2)
Anomalous dimensions for composite operators
77(1)
Group theory and the quark model
Unitary and hermitian matrices
78(1)
SU(n) matrices
79(1)
Reality of SU(2) representations
79(2)
An identity for unitary matrices
81(1)
An identity for SU(2) matrices
82(1)
SU(3) algebra in terms of quark fields
83(2)
Combining two spin 1/2 states
85(2)
The SU(2) adjoint representation
87(2)
Couplings of SU(2) vector representations
89(1)
Isospin breaking effects
90(3)
Spin wave function of three quarks
93(3)
Permutation symmetry in the spin-isospin space
96(1)
Combining two fundamental representations
97(3)
SU(3) invariant octet baryon-meson couplings
100(5)
Isospin wave functions of two pions
105(2)
Isospins in non-leptonic weak processes
107(3)
Chiral symmetry
Another derivation of Noether's current
110(1)
Lagrangian with second derivatives
111(2)
Conservation laws in a non-relativistic theory
113(2)
Symmetries of the linear σ-model
115(7)
Spontaneous symmetry breaking in the σ-model
122(1)
PCAC in the σ-model
123(3)
Non-linear σ-model I
126(2)
Non-linear σ-model II
128(2)
Non-linear σ-model III
130(3)
SSB by two scalars in the vector representation
133(3)
Renormalization and symmetry
Path-integral derivation of axial anomaly
136(4)
Axial anomaly and η &arrow; γγ
140(2)
Soft symmetry breaking and renormalizability
142(1)
Calculation of the one-loop effective potential
143(3)
The Parton model and scaling
The Gottfried sum rule
146(1)
Calculation of OPE Wilson coefficients
147(4)
σtot(e+e- &arrow; hadrons) and short-distance physics
151(4)
OPE of two charged weak currents
155(1)
The total decay rate of the W-boson
156(2)
Gauge symmetries
The gauge field in tensor notation
158(3)
Gauge field and geometry
161(2)
General relativity as a gauge theory
163(2)
O(n) gauge theory
165(2)
Broken generators and Goldstone bosons
167(2)
Symmetry breaking by an adjoint scalar
169(2)
Symmetry breaking and the coset space
171(1)
Scalar potential and first-order phase transition
172(1)
Superconductivity as a Higgs phenomenon
173(2)
Quantum gauge theories
Propagator in the covariant Rξ gauge
175(1)
The propagator for a massive vector field
176(1)
Gauge boson propagator in the axial gauge
177(1)
Gauge boson propagator in the Coulomb gauge
178(2)
Gauge invariance of a scattering amplitude
180(1)
Ward identities in QED
180(4)
Nilpotent BRST charges
184(2)
BRST charges and physical states
186(2)
Quantum chromodynamics
Colour factors in QCD loops
188(3)
Running gauge coupling in two-loop
191(2)
Cross-section for three-jet events
193(5)
Operator-product expansion of two currents
198(3)
Calculating Wilson coefficients
201(4)
Electroweak theory
Chiral spinors and helicity states
205(1)
The polarization vector for a fermion
206(2)
The pion decay rate and fπn
208(4)
Uniqueness of the standard model scalar potential
212(1)
Electromagnetic and gauge couplings
213(1)
Fermion mass-matrix diagonalization
214(1)
An example of calculable mixing angles
215(1)
Conservation of the B-L quantum number
216(2)
Electroweak phenomenology
Atomic parity violation
218(3)
Polarization asymmetry of Z &arrow; ff
221(1)
Simple τ-lepton decays
222(1)
Electron neutrino scatterings
223(2)
CP properties of kaon non-leptonic decays
225(1)
Z &arrow; HH is forbidden
226(1)
ΔI = 1/2 enhancement by short-distance QCD
227(3)
Scalar interactions and the equivalence theorem
230(4)
Two-body decays of a heavy Higgs boson
234(4)
Topics in flavourdynamics
Anomaly-free condition in a technicolour theory
238(1)
Pseudo-Goldstone bosons in a technicolour model
239(1)
Properties of Majorana fermions
239(5)
μ ey and heavy neutrinos
244(6)
Leptonic mixings in a vector-like theory
250(2)
Muonium-antimuonium transition
252(3)
Grand unification
Content of SU(5) representations
255(1)
Higgs potential for SU(5) adjoint scalars
256(2)
Massive gauge bosons in SU(5)
258(2)
Baryon number non-conserving operators
260(1)
SO(n) group algebra
260(3)
Spinor representations of SO(n)
263(4)
Relation between SO(2n) and SU(n) groups
267(2)
Construction of SO(2n) spinors
269(6)
Magnetic monopoles
The Sine-Gordon equation
275(5)
Planar vortex field
280(2)
Stability of soliton
282(1)
Monopole and angular momentum
283(6)
Instantons
The saddle-point method
289(3)
An application of the saddle-point method
292(3)
A Euclidean double-well problem
295(6)
References 301(2)
Index 303

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