Gauge theories in particle physics a practical introduction. Volume 1, From relativistic quantum mechanics to QED / Ian J. R. Aitchison and Anthony J. G. Hey.

Format:

Book

Author/Creator:

Aitchison, Ian J. R., author.

Hey, Anthony J. G., author.

Language:

English

Subjects (All):

Gauge fields (Physics).

Particles (Nuclear physics).

Weak interactions (Nuclear physics).

Physical Description:

1 online resource (979 pages)

Edition:

4th ed.

Place of Publication:

Boca Raton, Florida ; London, England ; New York : CRC Press, [2013]

Language Note:

English

Summary:

The fourth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories included in the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. In the first volume, a new chapter on Lorentz transformations and discrete symmetries presents a simple treatment of Lorentz transformations of Dirac spinors. Along with updating experimental results, this edition also introduces Majorana fermions at an early stage, making the material suitable for a first course in relativistic quantum mechanics. Covering much of the experimental progress made in the last ten years, the second volume remains focused on the two non-Abelian quantum gauge field theories of the Standard Model: QCD and the GSW electroweak theory. A new chapter on CP violation and oscillation phenomena describes CP violation in B-meson decays as well as the main experiments that have led to our current knowledge of mass-squared differences and mixing angles for neutrinos. Exploring a new era in particle physics, this edition discusses the exciting discovery of a boson with properties consistent with those of the Standard Model Higgs boson. It also updates many other topics, including jet algorithms, lattice QCD, effective Lagrangians, and three-generation quark mixing and the CKM matrix. This revised and updated edition provides a self-contained pedagogical treatment of the subject, from relativistic quantum mechanics to the frontiers of the Standard Model. For each theory, the authors discuss the main conceptual points, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight.

Contents:

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

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

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

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

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

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

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

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

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

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?

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

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

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

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.

Notes:

CC BY-NC-ND

Description based on print version record.

ISBN:

1-315-27525-2

1-4665-9112-9

9781315275253

OCLC:

1030993413