An Introduction to Gauge Theories.

Format:

Book

Author/Creator:

Cabibbo, N.

Contributor:

Maiani, L. (Luciano)

Benhar, Omar.

Language:

English

Subjects (All):

Gauge fields (Physics).

Field theory (Physics).

Physical Description:

1 online resource (290 pages)

Edition:

2nd ed.

Place of Publication:

Milton : Taylor & Francis Group, 2025.

Summary:

Written by world-leading experts in particle physics, this new book from Luciano Maiani and Omar Benhar, with contributions from the late Nicola Cabibbo, is based on Feynman's path integral formulation of quantum field theory.

Contents:

Cover

Half Title

Title Page

Copyright Page

Contents

Preface

The Authors

CHAPTER 1: INTRODUCTION

1.1. QUANTUM ELECTRODYNAMICS

1.2. UNITS AND OTHER CONVENTIONS.

CHAPTER 2: THE FEYNMAN PATH INTEGRAL

2.1. CALCULATION OF THE TRANSITION AMPLITUDE

2.2. THE LATTICE APPROXIMATION

2.3. THE CLASSICAL LIMIT

2.4. TIME AS A COMPLEX VARIABLE

2.5. STATISTICAL MECHANICS

2.6. GREEN'S FUNCTIONS

CHAPTER 3: TOWARDS A FIELD THEORY

3.1. THE GENERATING FUNCTIONAL

3.2. THE HARMONIC OSCILLATOR

3.3. FREE SCALAR FIELDS: PROPAGATOR AND GENERATING FUNCTIONAL

3.4. FREE SCALAR FIELD: ONE-PARTICLE STATES

3.5. CREATION AND DESTRUCTION OPERATORS

CHAPTER 4: EQUATIONS OF MOTION, SYMMETRIES AND WARD'S IDENTITY

4.1. SUM OVER PATHS AND OPERATORS

4.1.1. Derivatives

4.2. THE FUNDAMENTAL IDENTITY

4.3. QUANTUM MECHANICS

4.3.1. Equations of motion and commutation rules

4.3.2. Symmetries

4.3.3. The Hamiltonian function

4.4. FIELD THEORY

4.4.1. Symmetries in field theory

4.4.2. Ward's identity

4.5. THE SYMMETRIES OF THE VACUUM

CHAPTER 5: THE ELECTROMAGNETIC FIELD

5.1. THE CHOICE OF GAUGE

5.2. GENERATING FUNCTIONAL AND PROPAGATOR

5.3. SINGLE PHOTON STATES

5.4. VIRTUAL PHOTONS

CHAPTER 6: FERMION FIELDS

6.1. HARMONIC AND FERMI OSCILLATORS

6.1.1. Anticommuting variables

6.1.2. Sum over paths for the two oscillators

6.1.3. Gaussian integrals for commuting and anticommuting variables

6.2. QUANTISATION OF THE DIRAC FIELD

6.2.1. Fermion propagator

6.2.2. The spin-statistics theorem

6.2.3. One-particle states of the Dirac field

CHAPTER 7: SCATTERING PROCESSES AND THE S-MATRIX

7.1. "IN" STATES AND "OUT" STATES

7.2. SCATTERING AMPLITUDES AND THE S-MATRIX

7.3. CONSERVED QUANTITIES

7.4. THE LSZ REDUCTION FORMULAE.

CHAPTER 8: PERTURBATIVE GREEN'S FUNCTIONS IN λϕ4

8.1. THE PERTURBATIVE GENERATING FUNCTIONAL

8.2. FEYNMAN RULES FOR GREEN'S FUNCTIONS

8.3. CONNECTED PARTS AND VACUUM DIAGRAMS

8.4. PERTURBATIVE TWO-POINT GREEN'S FUNCTION

CHAPTER 9: S-MATRIX FEYNMAN DIAGRAMS IN λϕ4

9.1. ONE-PARTICLE IRREDUCIBLE DIAGRAMS

9.2. FEYNMAN RULES FOR THE S-MATRIX ELEMENTS

CHAPTER 10: QUANTUM ELECTRODYNAMICS

10.1. FEYNMAN DIAGRAMS FOR THE GENERATING FUNCTIONAL

10.2. TWO-POINT FUNCTIONS

10.3. REDUCTION FORMULAE

10.4. FEYNMAN DIAGRAMS FOR THE S-MATRIX

10.5. COMBINATORIALS

CHAPTER 11: RENORMALISATION OF QED

11.1. THE PHOTON PROPAGATOR

11.2. RENORMALISATION OF THE CHARGE

11.3. THE ELECTRON PROPAGATOR

11.3.1. The propagator to all orders

11.4. THE VERTEX

11.5. WARD'S IDENTITY

CHAPTER 12: APPLICATIONS OF QED

12.1. SCATTERING IN AN EXTERNAL FIELD

12.2. BREMSSTRAHLUNG AND INFRARED DIVERGENCE

12.3. THE LAMB SHIFT

12.4. VACUUM POLARISATION

12.4.1. Calculation of the tensor Πμν(k) to one loop

12.5. THE ANOMALOUS MAGNETIC MOMENT

12.5.1. Preliminaries

12.5.2. The calculation

CHAPTER 13: RENORMALISATION GROUP OF QED

13.1. EFFECTIVE ELECTRIC CHARGE

13.2. THE GELL.MANN AND LOW EQUATION

13.3. THE QED β FUNCTION

13.4. ASYMPTOTIC VARIATION OF THE EFFECTIVE CHARGE

CHAPTER 14: QUANTISING A NON-ABELIAN THEORY

14.1. FUNDAMENTALS

14.2. QUARKS IN QUANTUM CHROMODYNAMICS

14.3. THE FADDEEV.POPOV DETERMINANT

14.4. FEYNMAN RULES

CHAPTER 15: UNITARITY AND GHOSTS

15.1. THE CUTKOSKY RULE

15.2. THE INELASTIC REACTION u + u → d + d

15.3. THE CASE OF QED

15.4. NON-ABELIAN GAUGE THEORIES

CHAPTER 16: THE β FUNCTION IN QCD

16.1. VACUUM POLARISATION

16.2. CORRECTIONS TO QUARK PROPAGATOR AND VERTEX

16.3. ASYMPTOTIC FREEDOM

16.4. THE DETERMINATION OF αs.

16.5. THE LANDAU POLEAND THE CONTINUUM LIMIT OF GAUGE THEORIES

CHAPTER 17: LATTICE QCD

17.1. QCD FIELDS ON LATTICE

17.2. CHIRAL SYMMETRY WITH WILSON FERMIONS

17.3. LATTICE GREEN'S FUNCTIONS

17.4. LIGHT HADRON MASSES

17.5. LATTICE QCD VS. COMPUTING POWER

CHAPTER 18: The ΔI = 1/2 RULE IN STRANGE PARTICLES NON-LEPTONIC DECAYS

18.1. THE ΔI = 1/2 RULE IN K DECAYS

18.2. OPERATOR BASIS FOR NON-LEPTONIC DECAYS

18.3. QUARK STATISTICS AND THE ΔI = 1/2 RULE

18.4. QCD CORRECTIONS

18.5. THE CALLAN SZYMANZIK EQUATION

18.6. RELATIVE STRENGTHS OF NON-LEPTONIC OPERATORS

18.7. PENGUIN DIAGRAMS

18.8. WEAK INTERACTIONS IN LATTICE QCD

CHAPTER 19: THE WEAK MUON ANOMALY

19.1. THE R GAUGE

19.2. MUON ANOMALY: W EXCHANGE

19.3. Z AND HIGGS BOSON EXCHANGE

19.4. COMPARISON WITH DATA

CHAPTER 20: EFFECTIVE CONSTANTS AT HIGH ENERGY AND IDEAS ABOUT GRAND UNIFICATION

20.1. EFFECTIVE CONSTANTS OF THE STANDARD THEORY

20.2. GRAND UNIFICATION AND OTHER HYPOTHESES

CHAPTER 21: LIMITS ON THE MASS OF THE HIGGS BOSON

21.1. SCALAR FIELDS IN THE STANDARD THEORY

21.2. LIMITS ON THE MASS OF THE HIGGS BOSON

CHAPTER 22: EFFECTIVE POTENTIAL AND NATURALNESS

22.1. EFFECTIVE POTENTIAL

22.2. EXPANSION AROUND THE CLASSICAL LIMIT

22.3. LOOP EXPANSION OF THE POTENTIAL

22.4. ONE LOOP POTENTIAL IN THE STANDARD THEORY

22.5. NON-NATURALNESS OF THE STANDARD THEORY

APPENDIX A: TRANSITION AMPLITUDE CALCULATION

A.1. TRANSITION AMPLITUDE FOR ZERO POTENTIAL

APPENDIX B: CONNECTED DIAGRAMS

B.1. GENERATING FUNCTIONAL OF CONNECTED DIAGRAMS

APPENDIX C: LORENTZ INVARIANCE AND ONE-PARTICLE STATES

C.1. RENORMALISATION CONSTANTS

APPENDIX D: REDUCTION FORMULAE

D.1. REDUCTION FORMULAE FOR THE COMPTON SCATTERING AMPLITUDE

APPENDIX E: INTEGRALS

E.1. INTEGRATION IN D DIMENSIONS

E.2. FEYNMAN PARAMETERS.

APPENDIX F: CHIRAL SYMMETRY WITH WILSON FERMIONS: BASIC FORMULAE

F.1. A USEFUL IDENTITY

F.2. PARTIAL CONSERVATION OF THE AXIAL CURRENT

F.3. VACUUM SATURATION

F.4. SOFT PIONS AND NON-LEPTONIC AMPLITUDES

F.5. CHIRAL RELATIONS FOR K → π AND K → π π

APPENDIX G: β(λ) AND β(gt) FUNCTIONS

G.1. β(λ)

G.2. β(gt)

Bibliography

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

1-04-037030-6

1-003-56070-9

1-04-037027-6

OCLC:

1547907339