Cheng Ta-Pei, Li Ling-Fong. Gauge Theory of Elementary Particle Physics: Problems and Solutions

Clarendon Press, Oxford, 2000. — 315 p.Students of particle physics often find it difficult to locate resources to learn calculational techniques. Intermediate steps are not usually given in the research literature. To a certain extent, this is also the case even in some of the textbooks. In this book of worked problems we have made an effort to provide enough details so that a student starting in the field will understand the solution in each case. Our hope is that with this step-by-step guidance, students (after first attempting the solution themselves) can develop their skill, and confidence in their ability, to work out particle theory problems.Field quantization
Simple exercises in lambda-phi-4 theory
Auxiliary field
Disconnected diagrams
Simple external field problem
Path integral for a free particle
Path integral for a general quadratic action
Spreading of a wave packet
Path integral for a harmonic oscillator
Path integral for a partition function
Partition function for an SHO system
Non-standardpath-integralrepresentation
Weyl ordering of operators
Generating functional for a scalar field
Poles in Green's function
Renormalization
Counterterms in lambda-phi-4 theory and in QED
Divergences in non-linear chiral theory
Divergences in lower-dimensional field theories
n-Dimensional 'spherical' coordinates
Some integrals in dimensional regularization
Vacuum polarization and subtraction schemes
Renormalization of lambda-phi-3 theory in n dimensions
Renormalization of composite operators
Cutkosky rules
Renormalization group
Homogeneous renormalization-group equation
Renormalizatron constants
B-function for QED
Behaviour of g near a simple fixed point
Running coupling near a general fixed point
One-loop renormalization-group equation in massless lambda-phi-4 theory
B-function for the Yukawa coupling
Solving the renormarization-group equation by Coleman's method
Anomalous dimensions for composite operators
Unitary and hermitian matrices
SU(n) matrices
Reality of SU(2) representations
An identity for unitary matrices
An identity for SU(2) matrices
SU(3) algebra in terms of quark fields
Combining two spin-1/2 states
The SU(2) adjoint representation
Couplings of SU(2) vector representations
Isospin breaking effects
Spin wave function of three quarks
Permutation symmetry in the spin-isospin space
Combining two fundamental representations
SU(3) invariant octet baryon-meson couplings
Isospin wave functions of two pions
Isospins in non-leptonic weak processes
Chiral symmetry
Another derivation of Noether's current
Lagrangran with second derivatives
Conservation laws in a non-relativistic theory
Symmetries of the linear sigma-model
Spontaneous symmetry breaking in the sigma-model
PCAC in the sigma-model
Non-linear sigma-model l
Non-linear sigma-model II
Non-linear sigma-model III
SSB by two scalars in the vector representation
Renormalization and symmetry
Path-integral derivation of axial anomaly
Axial anomaly
Soft symmetry breaking and renormalizabllity
Calculation of the one-loop effective potential
The Parton model and scaling
The Gottfried sum rule
Calculation of OPE Wilson coefficients
sigma_tot(e+e- --> hadrons) and short-distance physics
OPE of two charged weak currents
The total decay rate of the W-boson
Gauge symmetries
The gauge field in tensor notation
Gauge field and geometry
General relativity as a gauge theory
O(n) gauge theory
Broken generators and Goldstone bosons
Symmetry breaking by an adjoint scalar
Symmetry breaking and the coset space
Scalar potential and first-order phase transition
Superconductivity as a Higgs phenomenon
Ouantum gauge theories
Propagator in the covariant Rksi gauge
The propagator for a massive vector field
Gauge boson propagator in the axial gauge
Gauge boson propagator in the Coulomb gauge
Gauge invariance of a scattering amplitude
Ward identities in QED
Nilpotent BRST charges
BRST charges and physical states
Ouantum chromodynamics
Colour factors in QCD loops
Running gauge coupling in two-loop
Cross-section for three-jet events
Operator-product expansion of two currents
Calculating Wilson coefficients
Electroweak theory
Chiral spinors and helicity states
The polartzation vector for a fermion
The pion decay rate and f_pi
Uniqueness of the standard model scalar potential
Electromagnetic and gauge couplings
Fermion mass-matrix diagonalization
An example of calculable mixing angles
Conservation of the B -- L quantum number
Electroweak phenomenology
Atomic parity violation
Polarization asymmetry of Z --> f f
Simple z-lepton decays
Electron neutrino scatterings
CP properties of kaon non-leptonic decays
Z --> H H is forbidden
DI = 1/2 enhancement by short-distance QCD
Scalar interactions and the equivalence theorem
Two-body decays of a heavy Higgs boson
Anomaly-free condition in a technicolour theory
Pseudo-Goldstone bosons in a technicolour model
Properties of Majorana fermions
mu --> e gammam and heavy neutrinos
Leptonic mixings in a vector-like theory
Muonium-antimuonium transition
Grand unification
Content of SU(5) representations
Higgs potential for SU(5) adjoint scalars
Massive gauge bosons in SU(5)
Baryon number non-conserving operators
SO(n) group algebra
Spinor representations of SO(n)
Relation between SO(2n) and SU(n)
Construction of SO(2n) spinors
Magnetic monopoles
The Sine-Gordon equation
Planar vortex field
Stability of soliton
Monopole and angular momentum
lnstantons
The saddle-point method
An application of the saddle-point method
A Euclidean double-well problem