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Define four-vectors and explain their properties under Lorentz transformations.

Compute the Lorentz-invariant spacetime interval between two events.

Define and manipulate the four-vectors for position, velocity, and momentum.

Calculate the invariant mass of a single particle and a system of particles.

Transform energy and momentum components between different inertial reference frames.

Derive the relativistic energy-momentum relation E² = (pc)² + (m₀c²)².

Explain the modern concept of mass as the Lorentz-invariant property of an object.

Apply the conservation of four-momentum to solve problems involving particle decays.

Apply the conservation of four-momentum to solve problems involving particle collisions.

Calculate the threshold energy required for particle production in a fixed-target experiment.

Classify the fundamental particles of the Standard Model: quarks, leptons, gauge bosons, and the Higgs boson.

Distinguish between fermions and bosons based on their spin.

Describe the four fundamental forces, their relative strengths, ranges, and mediating particles.

Identify which particles participate in each fundamental interaction.

Distinguish between fundamental particles and composite particles (hadrons: baryons and mesons).

State Noether's theorem and connect continuous symmetries to conserved quantities.

Apply the conservation of energy, momentum, charge, baryon number, and lepton number to determine if a reaction is allowed.

Describe the discrete symmetries of Charge Conjugation (C), Parity (P), and Time Reversal (T).

Explain the experimental observation of parity (P) violation in weak interactions.

Define CP symmetry and describe its violation in certain weak decays.

Explain the concept of isospin as an approximate symmetry of the strong interaction.

Distinguish between strong, electromagnetic, and weak interactions based on which quantities and symmetries are conserved.

List the six flavors of quarks and their primary properties (charge, mass).

Construct common baryons (qqq) and mesons (q-qbar) from up, down, and strange quarks.

Describe color charge as the fundamental charge of the strong interaction.

Explain the concepts of quark confinement and asymptotic freedom as key features of Quantum Chromodynamics (QCD).

Explain how deep inelastic scattering experiments provide evidence for quarks.

Describe how the production of particle jets in high-energy collisions provides evidence for quarks and gluons.

Explain the concept of virtual particles and propagators in quantum field theory.

Identify the basic components of a Feynman diagram: external lines, internal lines, and vertices.

State the fundamental interaction vertices for Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD).

Interpret simple, tree-level Feynman diagrams to describe a particle interaction process.

Draw the leading-order Feynman diagrams for basic QED processes, such as electron-electron scattering.

Draw the leading-order Feynman diagrams for basic strong interaction processes, such as quark-gluon scattering.

Describe the conceptual unification of the electromagnetic and weak forces.

Identify the W+, W-, and Z bosons and their roles in mediating weak interactions.

Distinguish between charged-current (W-mediated) and neutral-current (Z-mediated) weak interactions.

Draw leading-order Feynman diagrams for weak processes, such as beta decay and neutrino-electron scattering.

Explain the concept of spontaneous symmetry breaking in the context of a potential.

Describe how the Higgs mechanism generates mass for the W and Z bosons.

Describe how the Higgs mechanism generates mass for the fundamental fermions (quarks and leptons).

Summarize the complete particle content and interaction structure of the Standard Model.

Explain the role of gauge symmetry in constructing the Standard Model at a conceptual level.

List key experimental discoveries that provide evidence for the Standard Model (e.g., W/Z bosons, top quark, Higgs boson).

Describe the phenomenon of neutrino oscillations and its implication for neutrino mass.

Identify known limitations of and open questions beyond the Standard Model, such as the nature of dark matter and the hierarchy problem.