Particle Physics: The Standard Model
Gauge symmetry, QED, weak interactions, and the Standard Model
Stanford Continuing Studies • Winter 2010 • 10 lectures
Course Overview
This is the culmination of the Theoretical Minimum series - building the complete Standard Model of Particle Physics!
You'll learn how gauge symmetry - a seemingly abstract mathematical principle - generates all fundamental forces and predicts the existence of force-carrying particles.
🎯 What You'll Learn
- Gauge theory: Symmetry principles that determine interactions
- QED: U(1) gauge theory → electromagnetism
- Weak interactions: SU(2) gauge theory → W±, Z bosons
- Electroweak unification: SU(2)×U(1) → unified electromagnetic + weak
- Strong interactions: SU(3) gauge theory → QCD and quarks
- Higgs mechanism: How gauge bosons acquire mass
- The Standard Model: SU(3)×SU(2)×U(1) - complete theory!
Prerequisites: All previous Theoretical Minimum courses (special relativity, quantum mechanics, basic QFT concepts). This is the most advanced course in the series!
Course Topics
Gauge Symmetry & QED
The principle of local gauge invariance forces the existence of photons!
Starting from the Dirac equation and demanding invariance under local U(1) phase transformations ψ → eiα(x)ψ, we must introduce a gauge field Aμ (the photon) to maintain symmetry.
where Dμ = ∂μ + ieAμ is the covariant derivative. Gauge invariance determines the interaction!
Weak Interactions & SU(2)
Weak force (beta decay, neutrino interactions) comes from SU(2) gauge symmetry.
Three gauge bosons: W+, W-, W0. But there's a problem - weak force is short-range, so W bosons must be massive. Naive mass term breaks gauge invariance!
Solution: Spontaneous symmetry breaking via the Higgs mechanism. The Higgs field has nonzero vacuum expectation value, giving masses to W± and Z while keeping photon massless.
Strong Interactions & QCD
Quarks come in three colors (red, green, blue) - not actual colors, but quantum numbers transforming under SU(3) symmetry.
Eight gauge bosons (gluons) mediate the strong force. Unlike photons, gluons themselves carry color charge → gluons interact with gluons!
QCD has two remarkable properties: confinement (quarks never observed alone) and asymptotic freedom (interaction weakens at high energy).
The Complete Standard Model
Putting it all together: SU(3)C × SU(2)L × U(1)Y
- SU(3)C: Color symmetry → strong force (QCD)
- SU(2)L: Weak isospin → weak force (left-handed only!)
- U(1)Y: Hypercharge → electromagnetic + weak mixing
- Higgs field: Breaks SU(2)×U(1) → U(1)EM
This single framework explains:
- Why photons are massless but W/Z are heavy
- Why quarks combine into protons/neutrons but not free
- Why weak force violates parity (left-handed only)
- Why neutrinos interact so weakly
- How all forces unify at high energy
🔑 Key Concepts
Gauge Principle
Local symmetry transformations that depend on spacetime position. Requiring theory to be invariant under these forces the existence of gauge fields (force carriers)!
Spontaneous Symmetry Breaking
Lagrangian has a symmetry, but the vacuum state doesn't. Like a pencil balanced on its point - perfectly symmetric, but it must fall in some direction.
Higgs Mechanism
When gauge symmetry is spontaneously broken, gauge bosons "eat" Goldstone bosons and acquire mass. This gives mass to W± and Z while keeping photon massless.
Running Coupling
Coupling constants "run" with energy scale. QED coupling increases (charge screening). QCD coupling decreases at high energy (asymptotic freedom)!
Lectures 1-2: Particles, Fields & Quantum Chromodynamics
Video Lecture
Lecture 1: Particles, Fields and Forces
Introduction to Standard Model concepts and particle zoo (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Video Lecture
Lecture 2: Quantum Chromodynamics
Isospin, color charge, and gluon properties (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 1 introduces the theoretical framework underlying the Standard Model and provides a "zoological overview" of all observed particles - quarks, leptons, and force carriers.
Lecture 2 dives into quantum chromodynamics (QCD). Key topics:
- Isospin: Introduced by analogy to spin
- Color charge: Solution for Δ particles (uuu) - why three quarks can exist in same state
- Gluons: Properties described by analogy to quark-antiquark pairs
Lectures 3-4: Group Theory Foundation
Video Lecture
Lecture 3: Group Theory - Part 1
Basic concepts of group theory and connections to particle properties (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Video Lecture
Lecture 4: Group Theory - Part 2
Group generators, subgroups, gluons, and quark confinement (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
These two lectures develop the group theory framework essential for understanding gauge theories:
- Lecture 3: Basic group theory concepts connected to particle properties (spin, color)
- Lecture 4: Group generators and subgroups → particle structure
- Gluon properties: Explored with group theory framework
- Confinement: Why quarks are never observed alone
Lectures 5-6: Gauge Fields & The Weak Interaction
Video Lecture
Lecture 5: Gauge Fields and Symmetry
Gauge field concept, symmetries, and conserved charges (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Video Lecture
Lecture 6: The Weak Interaction
Why is the weak force weak? Propagators and Feynman diagrams (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 5 introduces the crucial concept of gauge fields and their symmetries:
- Symmetries → conserved charges (electric charge, color)
- Gauge principle: local symmetry forces existence of gauge bosons
- Connection to weak interactions
Lecture 6 answers the fundamental question: "Why is the weak force weak?"
- Propagator form in Feynman diagrams
- Massive W/Z bosons → short range
- Explicit vs spontaneous symmetry breaking (preview)
Lectures 7-8: Higgs Mechanism
Video Lecture
Lecture 7: Spontaneous Symmetry Breaking and Goldstone Bosons
How SSB in field theory creates Goldstone bosons (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Video Lecture
Lecture 8: The Higgs Field
Goldstone bosons eaten by gauge bosons to acquire mass (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
These lectures explain the Higgs mechanism - how gauge bosons acquire mass without breaking gauge invariance:
The Higgs Mechanism in Three Steps
- Spontaneous symmetry breaking: Field has symmetric Lagrangian but vacuum breaks symmetry
- Goldstone bosons: Massless particles from broken continuous symmetry
- "Eaten" Goldstone: Gauge bosons absorb Goldstone modes → become massive!
Lecture 7: Spontaneous symmetry breaking creates Goldstone bosons (like photons, gluons)
Lecture 8: The Goldstone boson gets "eaten", giving mass to gauge bosons via Higgs field
Lectures 9-10: Higgs & Fermions, Unification
Video Lecture
Lecture 9: The Higgs Field and Fermions
How the Higgs mechanism gives mass to fermions (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Video Lecture
Lecture 10: Renormalization and Unification
Running coupling constants and grand unification (Stanford)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 9 extends Higgs mechanism to fermions (quarks and leptons):
- Yukawa coupling: fermions interact with Higgs field
- Fermion masses proportional to coupling strength
- Why different fermions have different masses
Lecture 10 - the grand finale:
- Renormalization revisited: Running coupling constants
- Fermion masses: Mass generation mechanism
- W boson mass scale: Electroweak symmetry breaking
- Higgs mass expectations: Theoretical constraints
- Grand Unification: αEM, αweak, αstrong converge at ~1016 GeV!
🌟 The Unification Hint
All three coupling constants (electromagnetic, weak, strong) appear to unify at an energy scale of 1016 GeV when extrapolated using renormalization group equations.
This remarkable convergence suggests physics beyond the Standard Model - Grand Unified Theories (GUTs) where all forces merge into one!
🔗 Connection to MIT QFT Course
Susskind's Standard Model lectures provide crucial context for:
MIT Part IV: Quantum Electrodynamics
U(1) gauge theory - the simplest gauge theory
MIT Part V: Non-Abelian Gauge Theories
SU(N) gauge groups and Yang-Mills theory (Coming soon)
MIT Part VI: The Standard Model
Complete SM construction and phenomenology (Coming soon)
📚 Learning Path
- Master QED (MIT Part IV + Susskind)
- Understand gauge principle deeply (Susskind's physical approach)
- Learn non-Abelian gauge theory math (MIT Part V when available)
- See complete Standard Model (Susskind + MIT Part VI)
📖 Additional Resources
Full Lecture Playlist
All 10 lectures available free on YouTube
Search: "Leonard Susskind Particle Physics Standard Model 2010"
Recommended Reading
- Griffiths - Introduction to Elementary Particles: Undergraduate level, very clear
- Peskin & Schroeder - Introduction to QFT: Chapters on gauge theories
- Schwartz - QFT and the Standard Model: Complete modern treatment
- Weinberg - The Quantum Theory of Fields Vol II: Authoritative but advanced
- Cottingham & Greenwood - Introduction to the Standard Model: Phenomenology focus
Online Resources
- Particle Data Group (pdg.lbl.gov) - comprehensive particle physics data
- CERN educational resources on the Standard Model
- Quantum Diaries blog - physicist perspectives on SM physics
🏆 The Triumph of the Standard Model
The Standard Model is one of the most successful theories in science:
✅ Experimental Successes
- QED: 12 decimal place precision
- Weak force: W/Z bosons discovered 1983
- Top quark: predicted & found 1995
- Higgs boson: predicted 1960s, found 2012!
- Every LHC measurement consistent with SM
🔮 Predictions Confirmed
- Charm quark (1974)
- Tau lepton (1975)
- Bottom quark (1977)
- Gluons (1979)
- Top quark mass ~173 GeV
- Higgs mass ~125 GeV
"The Standard Model is a monument to the power of symmetry principles in physics. From the simple idea of gauge invariance, an entire universe of particles and forces emerges!" - Leonard Susskind