Lawrie I. A Unified Grand Tour of Theoretical Physics

Third Edition. — CRC Press, 2012. — 707 p.A Unified Grand Tour of Theoretical Physics invites its readers to a guided exploration of the theoretical ideas that shape our contemporary understanding of the physical world at the fundamental level. Its central themes, comprising space-time geometry and the general relativistic account of gravity, quantum field theory and the gauge theories of fundamental forces, and statistical mechanics and the theory of phase transitions, are developed in explicit mathematical detail, with an emphasis on conceptual understanding. Straightforward treatments of the standard models of particle physics and cosmology are supplemented with introductory accounts of more speculative theories, including supersymmetry and string theory.
This third edition of the Tour includes a new chapter on quantum gravity, focusing on the approach known as Loop Quantum Gravity, while new sections provide extended discussions of topics that have become prominent in recent years, such as the Higgs boson, massive neutrinos, cosmological perturbations, dark energy and matter, and the thermodynamics of black holes.
Designed for those in search of a solid grasp of the inner workings of these theories, but who prefer to avoid a full-scale assault on the research literature, the Tour assumes as its point of departure a familiarity with basic undergraduate-level physics, and emphasizes the interconnections between aspects of physics that are more often treated in isolation.Preface to the First Edition
Preface to the Second Edition
Glossary of Mathematical Symbols
Introduction: The Ways of Nature
Geometry
The Special and General Theories of Relativity
The Special Theory
The General Theory
Spacetime as a Differentiate Manifold
Topology of the Real Line R and of Rd
Differentiable Spacetime Manifold
Summary and Examples
Tensors
Extra Geometrical Structures
The Affine Connection
Geodesies
The Riemann Curvature Tensor
The Metric
The Metric Connection
What Is the Structure of Our Spacetime?
Classical Physics in Galilean and Minkowski Spacetimes
The Action Principle in Galilean Spacetime
Symmetries and Conservation Laws
The Hamiltonian
Poisson Brackets and Translation Operators
The Action Principle in Minkowski Spacetime
Classical Electrodynamics
Geometry in Classical Physics
More on Tensors
Differential Forms, Dual Tensors and Maxwell's Equations
Configuration Space and Its Relatives
The Symplectic Geometry of Phase Space
Hamiltonian Dynamics of Constrained Systems
A System with Second-Class Constraints
A System with a First-Class Constraint
General Constrained Systems
General Relativity and Gravitation
The Principle of Equivalence
Gravitational Forces
The Field Equations of General Relativity
The Gravitational Field of a Spherical Body
The Schwarzschild Solution
Time Near a Massive Spherical Body
Distances Near a Massive Spherical Body
Particle Trajectories Near a Massive Spherical Body
Black Holes
Schwarzschild Black Holes
Mass and Surface Gravity of a Schwarzschild Black Hole
Rotating Black Holes and Black-Hole Thermodynamics
Quantum Theory
Wave Mechanics
The Hilbert Space of State Vectors
Operators and Observable Quantities
Spacetime Translations and the Properties of Operators
Quantization of a Classical System
An Example: The One-Dimensional Harmonic Oscillator
Second Quantization and Quantum Field Theory
The Occupation-Number Representation
Field Operators and Observables
Lagrangian Formalism for Field Operators
Second Quantization for Fermions
Relativistic Wave Equations and Field Theories
The Klein-Gordon Equation
Scalar Field Theory for Free Particles
The Dirac Equation and Spin-| Particles
The Dirac Equation
Lorentz Covariance and Spin
Some Properties of the 7 Matrices
Conjugate Wavefunction and the Dirac Action
Probability Current and Bilinear Covariants
Plane-Wave Solutions
Massless Spin-| Particles
Spinor Field Theory
Weyl and Majorana Spinors
Particles of Spin 1 and 2
Photons and Massive Spin -1/2 Particles
Gravitons
Wave Equations in Curved Spacetime
Forces, Connections and Gauge Fields
Electromagnetism
Non-Abelian Gauge Theories
Non-Abelian Theories and Electromagnetism
Relevance of Non-Abelian Theories to Physics
The Theory of Kaluza and Klein
Interacting Relativistic Field Theories
Asymptotic States and the Scattering Operator
Reduction Formulae
Path Integrals
Path Integrals in Non-Relativistic Quantum Mechanics
Functional Integrals in Quantum Field Theory
Perturbation Theory
Quantization of Gauge Fields
Renormalization
Quantum Electrodynamics
The Coulomb Potential
Vacuum Polarization
The Lamb Shift
The Running Coupling Constant
Anomalous Magnetic Moments
Equilibrium Statistical Mechanics
Ergodic Theory and the Microcanonical Ensemble
The Canonical Ensemble
The Grand Canonical Ensemble
Relation between Statistical Mechanics and Thermodynamics
Quantum Statistical Mechanics
Field Theories at Finite Temperature
Black-Body Radiation
The Classical Lattice Gas
Analogies between Field Theory and Statistical Mechanics
Phase Transitions
Bose-Einstein Condensation
Critical Points in Fluids and Magnets
The Ising Model
Spontaneous Symmetry Breaking
The Ginzburg-Landau Theory
The Renormalization Group
The Ginzburg-Landau Theory of Superconductors
Spontaneous Breaking of Continuous Symmetries
Magnetic Effects in Superconductors
The Higgs Mechanism
Unified Gauge Theories of the Fundamental Interactions
The Weak Interaction
The Glashow-Weinberg-Salam Model for Leptons
Physical Implications of the Model for Leptons
Hadronic Particles in the Electroweak Theory
Quarks
Quarks in the Electroweak Theory
Colour and Quantum Chromodynamics
Loose Ends
The Higgs Boson
Massive Neutrinos
Grand Unified Theories
Supersymmetry
The Wess-Zumino Model
Superfields
Spontaneous Supersymmetry Breaking
The Supersymmetry Algebra
Supersymmetric Gauge Theories and Supergravity
Some Algebraic Details
Solitons and So On
Domain Walls and Kinks
The Sine-Gordon Solitons
Vortices and Strings
Magnetic Monopoles
The Early Universe
The Robertson-Walker Metric
The Friedmann-Lemaitre Models
Matter, Energy and the Age of the Universe
The Fairly Early Universe
Nucleosynthesis
Recombination and the Horizon Problem
The Flatness Problem
Density Perturbations
Field Equations for Linear Perturbations
Perturbations of Ideal Fluids
Adiabatic Perturbations
Qualitative Features of the CMBR Anisotropics
The Very Early Universe
Cosmological Phase Transitions
Inflation
Density Perturbations Generated during Inflation
0 Dark Energy and Dark Matter
An Introduction to String Theory
The Relativistic Point Particle
The Free Classical String
The String Action
Weyl Invariance and Gauge Fixing
The Euclidean Worldsheet and Conformal Invariance
Mode Expansions
A Useful Transformation
Quantization of the Free Bosonic String
The Quantum Virasoro Algebra
Quantum Gauge Fixing
The Critical Spacetime Dimension
The Ghost Hilbert Space
The BRST Cohomology
Physics of the Free Bosonic String
The Mass Spectrum
Vertex Operators
Strings and Quantum Gravity
Further Developments
String Interactions
Superstrings
The Ramifications of Compactification
Large Extra Dimensions
Gravity and Quantum Mechanics
Canonical Quantization of General Relativity
Hamiltonian Formulation of General Relativity
New Variables: Triads, Holonomies and Fluxes
Towards a Quantum Theory of Gravity
Quantum Cosmology
The Problem of Time
Loop Quantum Cosmology
Black-Hole Entropy
Some Snapshots of the Tour
Some Mathematical Notes
Delta Functions and Functional Differentiation
The Levi-Civita Tensor Density
Vector Spaces and Hilbert Spaces
Gauss' Theorem
Surface Area and Volume of a d-Dimensional Sphere
Gaussian Integrals
Grassmann Variables
Some Elements of Group Theory
Natural Units
Scattering Cross Sections and Particle Decay Rates