This book discusses particle physics and relativistic local field theory that is the main theoretical tool for analyzing particle physics. It is helpful for the professional physicist and to the serious graduate student of physics.
Preface to the Series
Preface
Part I: Introduction to Field Theory
Mechanics of a Finite System (Review)
Classical Mechanics
Quantization
Some General Theorems
The Spin-0 Field
General Discussion
Fourier Expansion (Free or Interacting Fields)
Hilbert Space (Free or Interacting Fields)
The Spin- Field
Mathematical Preliminaries
Free Field
Quantization (Free or Interacting Fields)
Fourier Expansion (Free or Interacting Fields)
Hilbert Space (Free or Interacting Fields)
Momentum and Angular Momentum Operators
Phase Factor Conventions between the Spinors
Two-component Theory
The Spin-1 Field (m0)
Free Field
Interacting Fields
Feynman Diagrams
Heisenberg, Schrödinger and Interaction Representations
S-Matrix
Time-ordered Products, Normal Products and Contractions
Perturbation Series
Wick Theorem
Applications
Differential Cross Sections for 1+2à 1’+2’ +…+n’
Quantum Electrodynamics
Lagrangian
Coulomb Gauge
Quantization
Photon Propagtor and Relativistic Invariance
Remarks
Solitons
Early History
Definition, Classification and Some General Remarks
One-space-dimensional Example
—Topological soliton. Nontopological soliton.
Derrick Theorem
Solitons vs. Plane Waves
—One Space-dimension. Two space-dimension. Three space-dimensions.
Quantization
—Lagrangian, Hamiltonian and commutation relations. Collective coordinates. Perturbation expansion.
Part II: Particle Physics
Order-of-magnitude Estimations
Radius of the Hydrogen Atom
Hadron Size
High-energy pp, p and Kp Total Cross Sections
e+ e- à μ+ + μ-
v + N à …
Compton Scattering
Mass Singularity and High-energy Behavior
e+ e- Pair Production by High-energy Photons
Part IIA: Particle Physics: Symmetry
General Discussion
Non-observables, Symmetry Transformations and Conservation Laws
Asymmetries and Observables
U1 Symmetry and P, C Invariance
QED as an Example
Applications
—Furry theorem. Positronium states. Decay of a spin-0 particleà 2y. Spin-1 particle 2y
General Discussion
Baryon Number and Lepton Number
Isotopic Spin and G Parity
Isospin
-U2 symmetry. Isospin transformations.
G Parity
—Nucleon-antinucleon system. The quantum number G.
Applications to Mesons and Baryons
—Pion. Vector mesons. ^ And kaon. Meson and baryon octets.
Isospin Violation
—Electromagnetic interaction. Weak interaction.
SU3 Symmetry
Mathematical Preliminary
—Tensors. Representations. Decomposition of ⑧×⑧. Some further properties. Excursion to other groups.
Hadron States and Their Flavor and Color Symmetries
—Pseudoscalar octet. Baryon spin octet and spin - decuplet.
Mass Formulas
—Hasym and the spurion formation. Octet mass formulas. Decuplet mass formula.
Time Reversal
Time Reversal in the Schrödinger Representation
Improbability of Constructing Time-reversed Quantum Solutions even for a Microscopic System
Properties of the T Operator
—QED as an example. Time reversal and angular momentum.
Time Reversal in Different Representations
—Heisenberg representation. Interaction representation.
T invariance of the S-matrix
Reciprocity
Reciprocity relations. Two-body reactions. Pion spin. Remarks.
Phase-angle Relations
-β decay. ^0 decay.
CPT Invariance
CPT Theorem
Applications
—Mass equality between particles and antiparticles. Opposite electromagnetic properties between particles and antiparticles. Lifetime equality between particles and antiparticles.
K-K System
Dalitz Plot
—Phase space. Boundary. Spin determination.
History
General Discussion of the Neutral Kaon Complex
—Mass and decay matrices. Eigenvalues. KSO and KLO
Interference Phenomena
T Violation
Analysis with the Assumption of CPT Invariance
—State vectors. KSO or KLO à π± + l± + vl or vl
Complementarity of Symmetry Violations
Phenomenological Analysis of the CP-nonconserving Interaction
—Milliweak. Superweak.
Vacuum As the Source of Asymmetry
What Is Vacuum?
Missing Symmetry
Vacuum Excitation
CP Nonconservation and Spontaneous Symmetry Breaking
Part IIB: Particle Physics: Interactions
Quark Confinement
The Problem
Color Dielectric Constant
A Hypothetical Problem in Classical Electromagnetism
A Phenomenological Explanation
—QCD vacuum as a perfect color dia-electric. Analogy with superconductivity. Remarks.
Quantum Chromodynamics and Gauge Theories
Non-Abelian Gauge Field Theories
An Example
—A simple mechanical model. = 0 gauge. X2= 0 gauge.
Quantization: V0= 0 Gauge
Coulomb gauge
—Coordinate transformation. Rigid-body roation. SU2 gauge field (classical). Quantum Hamiltonian.
Dia-electric (Antiscreening) Nature of the Vacuum
—SU2 gauge theory. Perturbative calculations.
Asymptotic Freedom
Path Integration
Cartesian Coordinates
—One-dimensional problem. From Hamiltonian operator to path integration. N-dimensional problem.
Weyl-ordered Hamiltonian
—From path integration to Hamiltonian operator.
Weyl-ordering.
Curvilinear Coordinates
—Hamiltonian operator. Path-integration formula. An example.
Feynman Diagrams
—Contraction. Connected and disconnected diagrams. Spin-0 field with interactions.
Fermions
—Grassmann algebra. Quantum mechanics. Path integration.
QCD
—Covariant gauge. Feynman rules in covariant gauge. Coulomb gauge.
Quark Model of Hadrons
Phenomenological Formulation
—Dielectric constant k. Energy density function U(σ). f-coupling
Hadrons as Solitons (Bags)
Approximate SU6 Symmetry
—Mass degeneracy. State vectors.
Zeroth-order Soliton Solutions
—Basic equations. Solutions. MIT bag. SLAC bag.
Applications to the Nucleon
—Charge radius. Magnetic moment gA/gV
First-order Corrections
—Gluon exchange and mass formulas. Quark masses.
Hadrons of Heavy Quarks
Weak Interactions
Purely Leptonic Interaction
—Phenomenological Lagrangian. Muon decay. Neutral lepton current.
Phenomenological Lagrangian for the Semileptonic Interaction
Πl2 and Kl2 Decays
—Pion decay. Kaon decay.
Classical (Nuclear) β Decay
—Charge symmetry. First and second class currents. CVC and the isotriplet current hypothesis. Experimental verification. Fermi constant in β decay.
Cabibbo Theory (including the GIM modification)
—Nuclear β decay. Πl2 and Kl2 decays. Strangeness nonconserving currents. β decay of the baryon octet. Leptonic decay of the D mesons.
High-energy Neutrino Reaction
—Kinematics. Structure functions.
Semileptonic Neutral-current Interaction
—∆S=0. High-energy neutrino reaction. Polarized electron scattering. Atomic parity violation.
Nonleptonic interaction
Intermediate Boson
—intermediate boson hypothesis. Limitation of Fermi theory.
Kobayashi-Maskawa Model
—Quark and lepton generations. Hadron current. U matrix. Experimental determination.
Weak and Electromagnetic Gauge Theory.
Nambu-goldstone and Higgs Mechanisms
—An example. Limit g=0. Higgs mechanism (g0). Unitary gauge.
Standard Model
—Gauge group. Lagrangian density. Spontaneous symmetry breaking. Lepton and gauge field coupling. Second order processes.
Extension to Hadrons
—GIM mechanism. Lagrangian density. Quark and gauge field coupling. Second order processes.
Quark-parton Model and High-energy Processes
Scaling Approximation
Quark-parton Model
—Parton picture. Quark-distribution functions.
Deep Inelastic e-nucleon Scattering
High-energy Neutrino Reaction
—Neutrino-quark cross sections. Neutrino-nucleon cross sections. Experimental results.
KLN Theorem
—First order perturbation. General case.
Applications to QED
—Infrared divergence. Mass singularities and jets. Radiative correction to μ decay.
Jets in QCD
—2-jet cross section. 3-jet events. Dalitz plot. 3-jet cross section. Correlations between jets.
Chiral Symmetry
Current Algebra
—Native commutators. Goto-Imamura-Schwinger modification.
CVC and CAC
Goldstone Theorem
Goldberger-Treiman Relation
—π decay amplitude. β decay of the nucleon. Generalization.
Low-energy πN Scattering
—Matrix element. Reduction. S-wave scattering length.
PCAC
—Chiral symmetry breaking. Relations between quark and pseudoscalar masses.
Outlook
—Size of leptons and quarks. Possibility of vacuum engineering. Improvement on conventional quantum mechanics.
Appendix
—Tables of Particle Properties. Plots of Cross Sections and Structure Functions
Index
Biography
A.G. Lee
