The course is organized into eight modules that move from the formal mathematical language of modern particle physics to the construction, phenomenology, and limitations of the Standard Model, and finally to an applied laboratory and project component.
Core topics: State space, operators, symmetries, invariants, and an introduction to group theory.
This module introduces the mathematical framework required for the formal description of fundamental interactions in particle physics. Students should develop fluency in the language of states and observables, linear operators, eigenvalue problems, commutation relations, symmetries, and invariants, together with a first exposure to continuous groups, generators, and Lie algebras. Particular emphasis should be placed on the idea that symmetries are not merely mathematical elegance, but the organizing principle behind conservation laws and the construction of quantum field theories, thereby preparing students for gauge theories later in the course.
Core topics: Lorentz group, spinors, the Dirac equation, and the interpretation of relativistic fermion fields.
This module presents the relativistic framework underlying the description of elementary particles. The content should include Lorentz transformations, four-vectors, relativistic covariance, spinor representations, Dirac matrices, and the Dirac equation, with special attention given to the physical interpretation of relativistic fermion fields and the description of spin-1/2 particles. The teaching should emphasize why spinors are required, how antiparticles emerge naturally in the relativistic theory, and how relativistic invariance constrains the construction of particle-physics models. In this way, the module prepares students for the field-theoretic formulation of the Standard Model.
Core topics: Local symmetries, QED as the Abelian example, followed by the gauge structure of the Standard Model: SU(3) × SU(2) × U(1).
This module develops the concept of gauge invariance as the fundamental principle governing the interactions of elementary particles. It should begin with the distinction between global and local symmetries, proceed through quantum electrodynamics as the simplest Abelian gauge theory, and then extend to non-Abelian gauge theories and the gauge structure of the Standard Model based on SU(3) × SU(2) × U(1). Emphasis should be placed on the logical construction of the Standard Model from symmetry requirements, field content, and local gauge invariance, so that students see the theory as a highly constrained framework rather than a collection of disconnected ingredients.
Core topics: Color charge, quarks and gluons, the QCD Lagrangian, non-Abelian gauge structure, gluon self-interactions, asymptotic freedom, confinement, hadrons, and selected collider applications.
This module introduces quantum chromodynamics (QCD) as the non-Abelian gauge theory of the strong interaction based on the symmetry group SU(3). The content should include color charge, quark and gluon fields as the fundamental degrees of freedom, the QCD Lagrangian, and the essential differences between Abelian and non-Abelian gauge theories. Particular emphasis should be placed on gluon self-interactions, the running of the strong coupling, asymptotic freedom at short distances, confinement at low energies, and the interpretation of hadrons as color-singlet states. The teaching should also introduce basic phenomenological concepts such as the parton model, hadronization, jet production, and the role of QCD in collider physics, so that students develop an understanding of both the formal structure and the experimental relevance of the strong interaction within the Standard Model.
Core topics: Spontaneous symmetry breaking, mass generation, the Higgs mechanism, and the basic properties of the Higgs boson.
This module discusses spontaneous symmetry breaking and its role in the generation of particle masses within the Standard Model. The content should include the distinction between symmetry of the Lagrangian and symmetry of the vacuum, the Higgs mechanism, electroweak symmetry breaking, Yukawa interactions, and mass generation for gauge bosons and fermions, including the physical interpretation of photon–Z mixing. The teaching should make clear that the Higgs sector is structurally necessary for the internal consistency of the Standard Model, while also connecting the formalism to the observed Higgs boson and its role in contemporary particle physics.
Core topics: Feynman diagrams, amplitudes, particle decays, cross sections, and selected physical observables.
This module introduces the basic phenomenological tools required to connect the formal structure of the Standard Model with experimentally measurable quantities. Students should be introduced to Feynman diagrams and Feynman rules, elementary tree-level amplitudes, particle decays, decay widths, branching ratios, scattering cross sections, and selected observables relevant to particle-physics experiments. The emphasis should be on interpretation rather than excessive technical detail, showing how predictions are extracted from the Lagrangian and why observables such as decay rates and cross sections are central to testing the theory.
Core topics: CP violation, unresolved conceptual and phenomenological issues, and the limitations of the Standard Model as a bridge to physics beyond the Standard Model.
This module presents selected conceptual and phenomenological limitations of the Standard Model. Topics may include CP violation, flavor structure, neutrino masses, dark matter, baryon asymmetry, the hierarchy problem, and other unresolved questions that reveal the boundaries of the theory. The purpose is not to turn the course into a full beyond-the-Standard-Model module, but rather to give students a clear understanding of both the successes and the incompleteness of the Standard Model, highlighting how open problems motivate current research in particle physics.
Core topics: Introduction to Python and ROOT/pyROOT, analysis of simulated or selected real data, preparation of a report, oral presentation, and final project discussion.
This module provides a practical introduction to selected computational and data-analysis techniques used in particle physics. It should include work with Python and ROOT/pyROOT, basic data handling, histogramming, visualization of distributions, simple fitting procedures, and the interpretation of simulated or selected experimental datasets. Students should apply the acquired knowledge in the form of a small project culminating in a written report and an oral presentation. The module is intended to strengthen the connection between formal theoretical concepts and their application in the analysis and interpretation of particle- physics data.