Theory and Detection of Magnetic Monopoles in Gauge Theories

The following sections are included:

• PREFACE

• CONTENTS

The magnetic monopole concept is a very old concept which probably started with the science of magnetism, and with the observation that a number of minerals (like magnetite) attracted pieces of iron. In fact, the word magnetism derives from the Magnesia region in Turkey where some of these minerals were found…

The following sections are included:

• Introduction

• The Dirac Monopole
  • Vector bundles
  • Dirac monopoles and charge quantization

• Non-abelian Monopoles
  • Monopoles of Dirac type in non-abelian gauge theories
  • Stability considerations for non-abelian monopoles
  • ’t Hooft-Polyakov monopoles(’t Hooft 1974, Polyakov 1974)
  • Configurations with spherical and axial symmetry
  • Monopoles break global Colour

• Dyons

• Completely Integrable Equations for Monopoles
  • The Bogomolny equation
  • The Lax pair
  • The patching function
  • Conjecture
  • The spectral curves of self-dual monopoles
  • A transformation to an ordinary differential equation
  • The asymptotic behaviour in x and z
  • The solution of the self-duality equation for T(z)
  • Arbitrary gauge groups
  • Examples
  • Bäcklund transformations
  • The moduli space of self-dual monopoles
  • The scattering of low energy monopoles
  • Perspectives

• References

The following sections are included:

• The Peculiar Angular Momentum States of Monopoles and Charged Particles

• QFT of Point Monopoles and Renormalization

• Quantum Fluctuations of a ’t Hooft-Polyakov monopole
  • Semiclassical method - a simple example
  • The quantum fluctuations of a ’t Hooft-Polyakov monopole
  • Constraints and collective coordinates
  • Path integral quantization

• Electron - Monopole Scattering
  • The partial wave analysis
  • The problem

• Fermions Coupled to a ’t Hooft-Polyakov Monopole
  • Introduction
  • The classical scattering problem
  • Jackiw-Rebbi zero modes
  • The quantum field theory
  • The Rubakov analysis
  • The cluster argument
  • Instantons, zero modes and the fermion vacuum
  • The induced instanton field near the monopole core
  • Callan’s bosonization approach
  • Presence of a θ-angle

• The Theory of Monopole Catalysis of Proton Decay
  • Introduction
  • The SU(5) monopole
  • Equivalent meson theory
  • Solution of the Dyson equation and the ’t Hooft equation for the SU(2)_c radial QCD
  • Exact solvability through the underlying Kac-Moody algebra
  • Baryon number violating correlation functions
  • Summary and comments on the simplifications

• Monopole - Proton Cross Sections
  • Introduction
  • The cross section σCAP
  • The cross section for catalysis
  • The cross section for P Mon + Mon + e⁺ + π⁰
  • The total cross section for catalysis

• Fermion - Grand Unified Monopole Systems as Solvable D = 2 QFT Problems
  • Introduction
  • The SU(5) monopole - fermion system
  • Calculation of rotator constant Ω
  • Analysis of rotator current interactions
  • Correlation functions and path integral
  • Monopoles with a more complex dyonic structure
  • The double charge SO(10) monopole
  • The double charge SU(4)⊗SU(2)_L⊗SU(2)_R monopole
  • Supersymmetric gauge theories

• Appendix A: Conventions and Notation
  • Dirac Algebra and Gamma Matrices
  • SU(N) Group and Matrices

• Appendix B: Exactly Solvable 2-Dimensional QFT’s
  • Introduction

• The Massless Schwinger Model

• Bosonization of Free Massless Fermion Fields in 1+1 Dimensions

• Heat Kernels and Fermion Determinants

• Kac-Moody Current Algebra’s and Non-linear Sigma Models

• Massless 2-dimensional Gauge Theories and Their Current Algebra

• Soliton Representations of Kac-Moody Algebra

• Calculation of Correlation Functions

• Bibliography

• ACKNOWLEDGMENTS

• REFERENCES

The following sections are included:

• BIG BANG COSMOLOGY
  • Hubble expansion (1929)
  • Cosmic Microwave Radiation Background
  • Helium Synthesis (Gamov et al.)

• PHASE TRANSITIONS IN GAUGE THEORIES
  • Baryon number-to-specific entropy ratio
  • Monopoles in Grand Unified Theories

• COSMOLOGICAL MONOPOLES

• MONOPOLE PRODUCTION IN GUT PHASE TRANSITION
  • References

• THE INFLATIONARY SCENARIO
  • References

• INFLATION WITH SU(5)
  • References

• INFLATION WITH HIGHER DIMENSIONAL THEORIES
  • References

• MAGNETIC MONOPOLES IN S0(10) AND E₆ GRAND UNIFIED THEORIES
  • References

• Conclusion

• Acknowledgements

The following sections are included:

• Introduction

• Galactic Magnetic Fields and the Parker Bound
  • The Quenching of the Galactic Magnetic Fields
  • Generation of the Galactic Magnetic Fields
  • Monopole Plasma Oscillation and Monopole-Dominated Galaxy Halo Models

• Astronomical Flux Limits on Monopoles which can Catalyze Proton Decay
  • Neutron Stars
  • Possible influence of the core
  • Pulsars
  • White dwarfs
  • Summary

• REFERENCES

Although we have covered the main areas in the theory and detection of magnetic monopoles, it was not possible to cover every topic, including the very complex and rapidly developing superstring approach to gravity and gauge fields, which may eventually provide a comprehensive unified theory of elementary particles and quantum gravity. Such theories also have monopole states, however, little is known about their properties at present. Already in the old Kaluza-Klein idea [see Kaluza (1922) and Klein (1926)] in which one gets Einstein gravity coupled to Maxwell’s electromagnetism from a pure gravity theory in 5 dimensions, there exist monopole states. These were recently pointed out by Gross and Perry (1983) and independently by Sorkin (1983). In these kinds of theories one starts with a pure gravity theory in 5 or higher dimensions and one looks for vacuum solutions, in which the extra dimensions are compactified, for example to circles. Then the motions of the extra metric components g_μ5 etc. over our 4-dimensional Minkowski space satisfy identical equations to gauge fields. The gauge invariance of these fields are simply a consequence of the Lorentz invariance in the extra dimensions. Such solutions for the vacuum sector are quite different from the singular Schwarzschild solutions, which represent dense lumps of matter in some spherically symmetric configuration. In the higher dimensional theories for example the 5-dimensional model of Kaluza, there exist spherically symmetric massive solutions, which are'non-singular and have a non-vanishing gauge field A_μ=g_μ5. Such solutions carry a magnetic charge , where R is the radius of the compactified dimension and G is the gravitational constant in 4 dimensions. The electric charge in this Kaluza-Klein theory is given by , so that eg = 1/2, i.e. the Dirac quantization condition is satisfied. The mass of this state is of order m = R/16πG = g²/4πR. Thus since the scale of compactification is the Planck mass, we expect the radius R ~ 1G⁻³² cm and m ~ 10¹⁹ GeV…

The following sections are included:

• Introduction

• Summary of the Properties of Magnetic Monopoles
  • Properties based on the Dirac relation
  • Properties of GUT monopoles

• Interaction of Monopoles with Matter
  • Introduction
  • The magnetic-monopole-magnetic-dipole interaction
  • Monopolic atoms and molecules
  • Nuclear reactions induced by magnetic monopoles
  • Energy losses of fast monopoles(β>10⁻²)
  • Energy losses of slow monopoles(10⁻⁴<β<10⁻²The fermi gas approximation
  • The Drell Effect
  • Energy losses at very low velocities(β<10⁻⁴
  • Energy losses in ferromagnetic materials
  • Energy losses in superconductors
  • Energy losses of monopoles in celestial bodies

• Monopole Detectors
  • Inductive Nonsuperconducting Coils
  • Superconducting induction devices
  • Scintillation counters
  • Gaseous detectors
  • Track-etch detectors
  • Other detectors

• Searches for “Classical” Monopoles
  • Accelerator searches
  • Searches in the cosmic radiation
  • Searches in bulk matter
  • Multi-γ events
  • Relevance of “classical” pole searches for larger mass poles

• Searches for GUT Monopoles
  • Introduction
  • Searches with superconducting induction devices
  • Counter searches
  • Searches in bulk matter
  • Searches with track-etch detectors

• Monopole Catalysis of Proton decay
  • Introduction
  • Searches for catalysis with proton decay detectors
  • Limit from neutrinos from the sun
  • Monopole catalysis of nucleon decay in the earth

• Other Types of searches
  • Introduction
  • Tachyon monopoles
  • Anomalous protons

• Outlook and Conclusions

• Acknowledgements

• REFERENCES