دانلود کتاب Gauge theories in particle physics : a practical introduction

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Cover
Volume 1
Cover
Half Title
Title Page
Copyright Page
Dedication Page
Contents
Preface
I Introductory Survey, Electromagnetism as a Gauge Theory, and Relativistic Quantum Mechanics
1 The Particles and Forces of the Standard Model
1.1 Introduction: the Standard Model
1.2 The fermions of the Standard Model
1.2.1 Leptons
1.2.2 Quarks
1.3 Particle interactions in the Standard Model
1.3.1 Classical and quantum fields
1.3.2 The Yukawa theory of force as virtual quantum exchange
1.3.3 The one-quantum exchange amplitude
1.3.4 Electromagnetic interactions
1.3.5 Weak interactions
1.3.6 Strong interactions
1.3.7 The gauge bosons of the Standard Model
1.4 Renormalization and the Higgs sector of the Standard Model
1.4.1 Renormalization
1.4.2 The Higgs boson of the Standard Model
1.5 Summary
Problems
2 Electromagnetism as a Gauge Theory
2.1 Introduction
2.2 The Maxwell equations: current conservation
2.3 The Maxwell equations: Lorentz covariance and gauge invariance
2.4 Gauge invariance (and covariance) in quantum mechanics
2.5 The argument reversed: the gauge principle
2.6 Comments on the gauge principle in electromagnetism
Problems
3 Relativistic Quantum Mechanics
3.1 The Klein–Gordon equation
3.1.1 Solutions in coordinate space
3.1.2 Probability current for the KG equation
3.2 The Dirac equation
3.2.1 Free-particle solutions
3.2.2 Probability current for the Dirac equation
3.3 Spin
3.4 The negative-energy solutions
3.4.1 Positive-energy spinors
3.4.2 Negative-energy spinors
3.4.3 Dirac’s interpretation of the negative-energy solutions of the Dirac equation
3.4.4 Feynman’s interpretation of the negative-energy solutions of the KG and Dirac equations
3.5 Inclusion of electromagnetic interactions via the gauge principle: the Dirac prediction of g = 2 for the electron
Problems
4 Lorentz Transformations and Discrete Symmetries
4.1 Lorentz transformations
4.1.1 The KG equation
4.1.2 The Dirac equation
4.2 Discrete transformations: P, C and T
4.2.1 Parity
4.2.2 Charge conjugation
4.2.3 CP
4.2.4 Time reversal
4.2.5 CPT
Problems
II Introduction to Quantum Field Theory
5 Quantum Field Theory I: The Free Scalar Field
5.1 The quantum field: (i) descriptive
5.2 The quantum field: (ii) Lagrange–Hamilton formulation
5.2.1 The action principle: Lagrangian particle mechanics
5.2.2 Quantum particle mechanics à la Heisenberg–Lagrange–Hamilton
5.2.3 Interlude: the quantum oscillator
5.2.4 Lagrange–Hamilton classical field mechanics
5.2.5 Heisenberg–Lagrange–Hamilton quantum field mechanics
5.3 Generalizations: four dimensions, relativity and mass
Problems
6 Quantum Field Theory II: Interacting Scalar Fields
6.1 Interactions in quantum field theory: qualitative introduction
6.2 Perturbation theory for interacting fields: the Dyson expansion of the S-matrix
6.2.1 The interaction picture
6.2.2 The S-matrix and the Dyson expansion
6.3 Applications to the ‘ABC’ theory
6.3.1 The decay C →A + B
6.3.2 A + B → A + B scattering: the amplitudes
6.3.3 A + B → A + B scattering: the Yukawa exchange mechanism, s and u channel processes
6.3.4 A + B → A + B scattering: the differential cross section
6.3.5 A + B → A + B scattering: loose ends
Problems
7 Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields; Introduction of Electromagnetic Interactions
7.1 The complex scalar field: global U(1) phase invariance, particles and antiparticles
7.2 The Dirac field and the spin-statistics connection
7.3 The Maxwell field Aμ(x)
7.3.1 The classical field case
7.3.2 Quantizing Aμ(x)
7.4 Introduction of electromagnetic interactions
7.5 P, C and T in quantum field theory
7.5.1 Parity
7.5.2 Charge conjugation
7.5.3 Time reversal
Problems
III Tree-Level Applications in QED
8 Elementary Processes in Scalar and Spinor Electrodynamics
8.1 Coulomb scattering of charged spin-0 particles
8.1.1 Coulomb scattering of s+ (wavefunction approach)
8.1.2 Coulomb scattering of s+ (field-theoretic approach)
8.1.3 Coulomb scattering of s−
8.2 Coulomb scattering of charged spin-½ particles
8.2.1 Coulomb scattering of e− (wavefunction approach)
8.2.2 Coulomb scattering of e−(field-theoretic approach)
8.2.3 Trace techniques for spin summations
8.2.4 Coulomb scattering of e+
8.3 e−s+ scattering
8.3.1 The amplitude for e−s+ → e−s+
8.3.2 The cross section for e−s+ → e−s+
8.4 Scattering from a non-point-like object: the pion form factor in e−π+ → e−π+
8.4.1 e− scattering from a charge distribution
8.4.2 Lorentz invariance
8.4.3 Current conservation
8.5 The form factor in the time-like region: e+e− → π+π− and crossing symmetry
8.6 Electron Compton scattering
8.6.1 The lowest-order amplitudes
8.6.2 Gauge invariance
8.6.3 The Compton cross section
8.7 Electronmuon elastic scattering
8.8 Electron–proton elastic scattering and nucleon form factors
8.8.1 Lorentz invariance
8.8.2 Current conservation
Problems
9 Deep Inelastic Electron–Nucleon Scattering and the Parton Model
9.1 Inelastic electron–proton scattering: kinematics and structure functions
9.2 Bjorken scaling and the parton model
9.3 Partons as quarks and gluons
9.4 The Drell–Yan process
9.5 e+e− annihilation into hadrons
Problems
IV Loops and Renormalization
10 Loops and Renormalization I: The ABC Theory
10.1 The propagator correction in ABC theory
10.1.1 The O(g2) self-energy ∏[2]C (q2)
10.1.2 Mass shift
10.1.3 Field strength renormalization
10.2 The vertex correction
10.3 Dealing with the bad news: a simple example
10.3.1 Evaluating ∏[2]C (q2)
10.3.2 Regularization and renormalization
10.4 Bare and renormalized perturbation theory
10.4.1 Reorganizing perturbation theory
10.4.2 The O(g2ph) renormalized self-energy revisited: how counter terms are determined by renormalization conditions
10.5 Renormalizability
Problems
11 Loops and Renormalization II: QED
11.1 Counter terms
11.2 The O(e2) fermion self-energy
11.3 The O(e2) photon self-energy
11.4 The O(e2) renormalized photon self-energy
11.5 The physics of ∏̅γ[2] (q2)
11.5.1 Modified Coulomb’s law
11.5.2 Radiatively induced charge form factor
11.5.3 The running coupling constant
11.5.4 ∏̅γ[2] in the s-channel
11.6 The O(e2) vertex correction, and Z1 = Z2
11.7 The anomalous magnetic moment and tests of QED
11.8 Which theories are renormalizable – and does it matter?
Problems
A Non-relativistic Quantum Mechanics
B Natural Units
C Maxwell’s Equations: Choice of Units
D Special Relativity: Invariance and Covariance
E Dirac δ-Function
F Contour Integration
G Green Functions
H Elements of Non-relativistic Scattering Theory
H.1 Time-independent formulation and differential cross section
H.2 Expression for the scattering amplitude: Born approximation
H.3 Time-dependent approach
I The Schrödinger and Heisenberg Pictures
J Dirac Algebra and Trace Identities
J.1 Dirac algebra
J.1.1 γ matrices
J.1.2 γ5 identities
J.1.3 Hermitian conjugate of spinor matrix elements
J.1.4 Spin sums and projection operators
J.2 Trace theorems
K Example of a Cross Section Calculation
K.1 The spin-averaged squared matrix element
K.2 Evaluation of two-body Lorentz-invariant phase space in ‘laboratory’ variables
L Feynman Rules for Tree Graphs in QED
L.1 External particles
L.2 Propagators
L.3 Vertices
References
Index
Volume 2
Cover
Half Title
Title Page
Copyright Page
Dedication Page
Contents
Preface
V Non-Abelian Symmetries
12 Global Non-Abelian Symmetries
12.1 The Standard Model
12.2 The flavour symmetry SU(2)f
12.2.1 The nucleon isospin doublet and the group SU(2)
12.2.2 Larger (higher-dimensional) multiplets of SU(2) in nuclear physics
12.2.3 Isospin in particle physics: flavour SU(2)f
12.3 Flavour SU(3)f
12.4 Non-Abelian global symmetries in Lagrangian quantum field theory
12.4.1 SU(2)f and SU(3)f
12.4.2 Chiral symmetry
Problems
13 Local Non-Abelian (Gauge) Symmetries
13.1 Local SU(2) symmetry
13.1.1 The covariant derivative and interactions with matter
13.1.2 The non-Abelian field strength tensor
13.2 Local SU(3) Symmetry
13.3 Local non-Abelian symmetries in Lagrangian quantum field theory
13.3.1 Local SU(2) and SU(3) Lagrangians
13.3.2 Gauge field self-interactions
13.3.3 Quantizing non-Abelian gauge fields
Problems
VI QCD and the Renormalization Group
14 QCD I: Introduction, Tree Graph Predictions, and Jets
14.1 The colour degree of freedom
14.2 The dynamics of colour
14.2.1 Colour as an SU(3) group
14.2.2 Global SU(3)c invariance, and ‘scalar gluons’
14.2.3 Local SU(3)c invariance: the QCD Lagrangian
14.2.4 The θ-term
14.3 Hard scattering processes, QCD tree graphs, and jets
14.3.1 Introduction
14.3.2 Two-jet events in p̅p collisions
14.3.3 Three-jet events in p̅p collisions
14.4 3-jet events in e+e− annihilation
14.4.1 Calculation of the parton-level cross section
14.4.2 Soft and collinear divergences
14.5 Definition of the two-jet cross section in e+e− annihilation
14.6 Further developments
14.6.1 Test of non-Abelian nature of QCD in e+e− → 4 jets
14.6.2 Jet algorithms
Problems
15 QCD II: Asymptotic Freedom, the Renormalization Group, and Scaling Violations
15.1 Higher-order QCD corrections to σ(e+e− → hadrons): large logarithms
15.2 The renormalization group and related ideas in QED
15.2.1 Where do the large logs come from?
15.2.2 Changing the renormalization scale
15.2.3 The RGE and large −q2 behaviour in QED
15.3 Back to QCD: asymptotic freedom
15.3.1 One loop calculation
15.3.2 Higher-order calculations, and experimental comparison
15.4 σ(e+e− → hadrons) revisited
15.5 A more general form of the RGE: anomalous dimensions and running masses
15.6 QCD corrections to the parton model predictions for deep inelastic scattering: scaling violations
15.6.1 Uncancelled mass singularities at order αs
15.6.2 Factorization, and the order αs DGLAP equation
15.6.3 Comparison with experiment
Problems
16 Lattice Field Theory, and the Renormalization Group Revisited
16.1 Introduction
16.2 Discretization
16.2.1 Scalar fields
16.2.2 Dirac fields
16.2.3 Gauge fields
16.3 Representation of quantum amplitudes
16.3.1 Quantum mechanics
16.3.2 Quantum field theory
16.3.3 Connection with statistical mechanics
16.4 Renormalization, and the renormalization group, on the lattice
16.4.1 Introduction
16.4.2 Two one-dimensional examples
16.4.3 Connections with particle physics
16.5 Lattice QCD
16.5.1 Introduction, and the continuum limit
16.5.2 The static qq̅ potential
16.5.3 Calculation of α(M2Z)
16.5.4 Hadron masses
Problems
VII Spontaneously Broken Symmetry
17 Spontaneously Broken Global Symmetry
17.1 Introduction
17.2 The Fabri–Picasso theorem
17.3 Spontaneously broken symmetry in condensed matter physics
17.3.1 The ferromagnet
17.3.2 The Bogoliubov superfluid
17.4 Goldstone’s theorem
17.5 Spontaneously broken global U(1) symmetry: the Goldstone model
17.6 Spontaneously broken global non-Abelian symmetry
17.7 The BCS superconducting ground state
Problems
18 Chiral Symmetry Breaking
18.1 The Nambu analogy
18.1.1 Two flavour QCD and SU(2)f L×SU(2)f R
18.2 Pion decay and the Goldberger–Treiman relation
18.3 Effective Lagrangians
18.3.1 The linear and non-linear σ-models
18.3.2 Inclusion of explicit symmetry breaking: masses for pions and quarks
18.3.3 Extension to SU(3)f L×SU(3)f R
18.4 Chiral anomalies
Problems
19 Spontaneously Broken Local Symmetry
19.1 Massive and massless vector particles
19.2 The generation of ‘photon mass’ in a superconductor: Ginzburg–Landau theory and the Meissner effect
19.3 Spontaneously broken local U(1) symmetry: the Abelian Higgs model
19.4 Flux quantization in a superconductor
19.5 ’t Hooft’s gauges
19.6 Spontaneously broken local SU(2) × U(1) symmetry
Problems
VIII Weak Interactions and the Electroweak Theory
20 Introduction to the Phenomenology of Weak Interactions
20.1 Fermi’s ‘current–current’ theory of nuclear β-decay, and its generalizations
20.2 Parity violation in weak interactions, and V-A theory
20.2.1 Parity violation
20.2.2 V-A theory: chirality and helicity
20.3 Lepton number and lepton flavours
20.4 The universal current × current theory for weak interactions of leptons
20.5 Calculation of the cross section for νμ + e− → μ− + νe
20.6 Leptonic weak neutral currents
20.7 Quark weak currents
20.7.1 Two generations
20.7.2 Deep inelastic neutrino scattering
20.7.3 Three generations
20.8 Non-leptonic weak interactions
Problems
21 CP Violation and Oscillation Phenomena
21.1 Direct CP violation in B decays
21.2 CP violation in B meson oscillations
21.2.1 Time-dependent mixing formalism
21.2.2 Determination of the angles α(φ2) and β(φ1) of the unitarity triangle
21.3 CP violation in neutral K-meson decays
21.4 Neutrino mixing and oscillations
21.4.1 Neutrino mass and mixing
21.4.2 Neutrino oscillations: formulae
21.4.3 Neutrino oscillations: experimental results
21.4.4 Matter effects in neutrino oscillations
21.4.5 Further developments
Problems
22 The Glashow–Salam–Weinberg Gauge Theory of Electroweak Interactions
22.1 Difficulties with the current–current and ‘naive’ IVB models
22.1.1 Violations of unitarity
22.1.2 The problem of non-renormalizability in weak interactions
22.2 The SU(2) × U(1) electroweak gauge theory
22.2.1 Quantum number assignments; Higgs, W and Z masses
22.2.2 The leptonic currents (massless neutrinos): relation to current–current model
22.2.3 The quark currents
22.3 Simple (tree-level) predictions
22.4 The discovery of the W± and Z0 at the CERN pp̅ collider
22.4.1 Production cross sections for W and Z in pp̅ colliders
22.4.2 Charge asymmetry in W± decay
22.4.3 Discovery of theW± and Z0 at the pp̅ collider, and their properties
22.5 Fermion masses
22.5.1 One generation
22.5.2 Three-generation mixing
22.6 Higher-order corrections
22.7 The top quark
22.8 The Higgs sector
22.8.1 Introduction
22.8.2 Theoretical considerations concerning mH
22.8.3 Higgs boson searches and the 2012 discovery
Problems
M Group Theory
M.1 Definition and simple examples
M.2 Lie groups
M.3 Generators of Lie groups
M.4 Examples
M.4.1 SO(3) and three-dimensional rotations
M.4.2 SU(2)
M.4.3 SO(4): The special orthogonal group in four dimensions
M.4.4 The Lorentz group
M.4.5 SU(3)
M.5 Matrix representations of generators, and of Lie groups
M.6 The Lorentz group
M.7 The relation between SU(2) and SO(3)
N Geometrical Aspects of Gauge Fields
N.1 Covariant derivatives and coordinate transformations
N.2 Geometrical curvature and the gauge field strength tensor
O Dimensional Regularization
P Grassmann Variables
Q Feynman Rules for Tree Graphs in QCD and the Electroweak Theory
Q.1 QCD
Q.1.1 External particles
Q.1.2 Propagators
Q.1.3 Vertices
Q.2 The electroweak theory
Q.2.1 External particles
Q.2.2 Propagators
Q.2.3 Vertices
References
Index