SPFCU24

UE Standard model and gauge theory

Unité d'enseignement (UE) de 4 crédits

^En UE enseignée en Anglais

Contenu

1st part: Gauge Theories
Motivations:
• Notion of symmetry: within the framework of geometry or differential algebra.
• There is a strong link between geometry and physics.
• Symmetries confer a structure to spaces, give conserved quantities (Noether)
• In Quantum Mechanics: gauge transformation of the 4-potential vs unitary transformation
• Gauge principle in field theory: covariant derivative, coupling matter to Maxwell gauge potential (→ Yang-Mills theories.)
• Analytical Mechanics and symplectic geometry (geometric quantization)
• General Relativity : Riemann geometry, diffeomorphisms
Covered issues:
- Why the notion of fiber bundles appears in Physics? The very important role of Lie groups
- Which geometric interpretation to give to:
• the Yang-Mills potential? / to the Christoffel symbols? Notion of connection.
• the Yang-Mills field? / to the Riemann tensor? Notion of curvature.
- How to view the notion of connection? get an image of a gauge choice (local description)
- What about representations of Lie groups? Associated fiber bundles.
- What geometrical meaning for the matter fields? Notion of smooth sections.
- What is a gauge group? (gauge transformations? gauge fixing?)
- How to formulate a gauge theory in terms of geometrical concepts?
- How to translate an infinitesimal symmetry in algebraic terms? Notion of differential algebra
- Differential geometry & differential algebra: an elegant unifying language for all theories? (Yang-Mills, gravitation, ...)

2nd part: The Standard Model of Particle Physics: Emphasis on symmetries and applications to the standard model.
Successes of the standard model
• Consistent (unitary and renormalizable) theory
• Weak neutral currents and gauge bosons
• High energy chromodynamics
• P and CP violation
• Cancellation of chiral anomalies
• Higgs boson
Challenges to the Standard model of Particle Physics
• Derivation of confinement and hadronic physics
• Hierarchy of masses (electron mass = 0.5 MeV; top mass = 173 GeV)
• Status of massive neutrinos
• Number of free parameters ≥ 18
• Fine tuning of the Higgs mass
Topics
• One loop β function, asymptotic freedom
• Construction of the standard model (including massive neutrinos)
• Physical consequences (CP violation, low and high energy behavior in QCD, ....)
• Physics beyond the standard model

UE Standard model and gauge theory

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