Particles, Fields and Forces: A Conceptual Guide to Quantum Field Theory and the Standard Model

Contents
1 Introduction
2 Particles or Waves?
2.1 How to Describe a Wave
2.1.1 Wavelength Represents Momentum
2.1.2 Frequency Represents Energy
2.1.3 Superposition and Interference of Waves
2.1.4 Measurement
2.2 Probability Amplitude
2.3 What Is Waving?
3 Fields and Waves Making Up Reality
3.1 What Is a Field?
3.2 All We Are Is Waves in a Field
3.2.1 Objection 1: How Can a Billiard Ball Be a Wave?
3.2.2 Objection 2: But Things Do Not Look Like Waves
3.2.3 Objection 3: How Can Waves Make a Table Seem Massive?
3.2.4 Objection 4: But Waves Die Out, Don’t They?
3.2.5 Objection 5: What, Then, Is Empty Space, Through Which I Can Throw a Ball?
3.2.6 Objection 6: Oh-No, Not the Ether Again…
3.3 Conclusion
4 What Is a Particle If It Is a Wave?
4.1 Where Is a Particle?
4.2 Waves in Space
4.3 Waves in Space and the Double Slit Experiment
4.4 Waves in Time
4.5 A Particle Is a Bunch of Waves
4.6 Velocity of Particles and Waves
5 The Potential of a Field’s Elasticity
5.1 Exchanging Energy in a Field
5.2 Waves in a Medium
6 A Wave of Relativity
6.1 Wave Velocity
6.2 How Does a Wave Become Massive?
6.2.1 A Game with Rope and Springs
6.2.2 Consequence 1: You Cannot Go Faster Than Light
6.2.3 Consequence 2: The Relation Between Frequency and Wavelength Depends on the Mass
6.2.4 Consequence 3: Mass = Inertia
6.2.5 Consequence 4: Other Potential Differences Can Create “Mass”
6.2.6 Consequence 5: Mass Can Be Changed Into Energy
6.2.7 Example: Photons in a Plasma
6.2.8 Conclusion and Summary
6.3 The Elasticity of the Minkowski Metric
6.4 Length Contraction and Time Dilation of Waves
6.5 About Higgs
7 Quantization of Fields
7.1 First Quantization
7.2 Second Quantization
7.3 Phonons
7.4 Conclusion
8 Energy in Waves and Fields
8.1 Conservation Laws
8.1.1 Energy—Momentum Tensor
8.2 How to Envision a Field Quantum
8.2.1 Coupled Oscillators
8.3 Annihilation of a Field Quantum
8.4 Describing a Field Quantum
9 Symmetry and the Origin of Force
9.1 Rotational Symmetry
9.1.1 Rotations in a Plane
9.1.2 Rotations in Three Dimensions
9.1.3 Rotations in Eight Dimensions
9.2 The Electromagnetic Field
9.2.1 QED
9.2.2 The Electromagnetic Field
9.3 Path Integral
9.4 How Does Symmetry Create a Force?
9.5 A Constant Field and the Refractive Index
9.6 Conclusion Regarding the Electromagnetic Force
10 Propagators and Virtual Particles
10.1 Time Order of Events and Feynman Diagrams
10.2 Propagator
10.3 Relation Between Virtual and Real Particles
10.3.1 Summarizing
10.4 What Is an Electron Really?
10.5 How Do Virtual Particles Create a Force?
10.5.1 Electrons of Equal Charge
10.5.2 An Electron and a Positron
10.5.3 Conclusion
10.6 Path Integral Revisited
10.7 Fluctuating Fields
10.7.1 Casimir effect
10.8 The Arrow of Time
11 Renormalisation of Fearful Infinities
11.1 Renormalizing Mass
11.2 Renormalizing Charge
11.3 Renormalisation Group
12 Is the Cat Dead or Alive? How Quantum Decoherence ‘Digitized’ the Universe
12.1 Quantum De-Coherence and “Collapse of the Wave Function”
12.1.1 Entanglement
12.1.2 Quantum Decoherence
12.1.3 The Transition from Quantum Behaviour to Classical Behaviour
12.2 Tunnelling and Decoherence
12.3 Quantum Computing
12.4 Schrödinger’s Cat
13 Spin Makes Up Bosons and Fermions
13.1 What Is Spin?
13.1.1 Orbital Momentum in the Atom
13.1.2 The Origin of Spin
13.1.3 Spin as a Wave
13.2 Fermions and Bosons
13.2.1 Wave Phase
13.2.2 Fermions
13.2.3 Bosons
13.2.4 Spinor Fields
13.2.5 Fermions in Opposite Spin
13.3 Helicity
13.4 Chirality
13.4.1 Fermions Come with Two Chiralities, Called Left and Right. Bosons Do Not
13.4.2 Under Parity, the Chirality of a Fermion Is Swapped to the Opposite Chirality
13.4.3 Low Velocity Fermions Flip Chirality at the Frequency of Their Mass
13.4.4 Chirality Is Not the Same as Spin
13.4.5 Fermions of Different Chirality Are Different Particles
13.4.6 At Very High Velocities, the Chirality of Fermions Becomes Fixed and Related to Their Helicity
13.5 Fermions Becoming Bosons
13.6 Conclusions on Spin, Helicity, and Chirality
14 Conservation of Charge and Particle Number
14.1 Particle Number Conservation
14.2 Charge Conservation
15 Particle Zoo
15.1 A Visit to the Particle Zoo
15.2 Introducing the Fundamental Particle Overview
15.3 The Rabbit Hole
16 Electroweak Force in the Early Universe
16.1 The First 10−12 s
16.1.1 Electron and Neutrino Waves
16.1.2 Introducing the Original U(1) Gauge Field
16.2 Symmetry Amongst the Waves
16.2.1 Introducing the SU(2) Gauge Field
16.2.2 Including Isospin Symmetry in the Overview of Waves
16.3 Introducing the Higgs Field
16.3.1 Fields Overview First 10−12 s
16.4 Fundamental Particle Overview 2
17 Symmetry Breaking and the World Was Never the Same Again
17.1 Mixing Fields
17.1.1 What Condensates in the Vacuum?
17.2 Breaking the Symmetry of the Higgs Field
17.2.1 Consequences for the U(1) and SU(2) Gauge Bosons
17.2.2 Mass of the W−, W+ and Z°
17.2.3 Consequences for the Fermion Interaction Potentials
17.3 Interactions
17.3.1 Photon Interactions
17.3.2 W-Interactions
17.3.3 Z-Interactions
17.3.4 Z-W Self-interactions
17.3.5 Neutron Decay
17.3.6 Radioactive Decay
17.3.7 Cabibbo Rotation
17.3.8 Neutrino Oscillations
17.3.9 Concluding
17.4 Fermions Gaining Mass
17.5 Parity Violation and CPT Symmetry
17.6 Family Business
17.7 Fundamental Particle Overview 3
18 The Strong Force: Quantum Chromodynamics
18.1 The Big Why
18.2 The Colour Symmetry
18.3 QCD Fields: Overview
18.3.1 Colour Confinement
18.3.2 Quark Jets
18.3.3 Asymptotic Freedom
18.4 Composite Particles
18.5 Interactions
18.5.1 Quark–Quark Colour Interactions
18.5.2 Annihilation and Creation
18.5.3 Gluon–Gluon Interactions
18.5.4 Proton–Anti-proton Collisions
18.5.5 Residual Strong Force or “Nuclear Force”
18.6 Masses of Quarks, Mesons, and Baryons
18.7 Fundamental Particle Overview 4
19 Gravity as a Field
19.1 A Field Theory of Gravity
19.2 Background Independence
19.3 Other Problems
20 Further Reading
20.1 Pop Science
20.2 The Internet
References and Sources
Index