How perturbation theory actually computes the field strength renormalization Z and the shift from bare mass m₀ to physical mass m, by resumming all 1PI insertions into the full propagator i/(p² − m₀² − M²(p²)).

A non-perturbative derivation showing that the analytic structure of the interacting two-point function forces field strength renormalization Z and a physical mass m ≠ m₀ — long before any loops or infinities appear.

A practical companion to a video I made in collaboration with STARGAZER on beginning the MSc Physics program at Heidelberg University — covering courses, research groups, admin, and life in the city.

Exploring the Poincaré group, its Casimir operators, and Wigner's classification of elementary particles by mass and spin/helicity.

Decomposing the Lorentz algebra into su(2) ⊕ su(2), classifying representations by (j+, j-), and understanding Weyl, Dirac, and Majorana spinors in relativistic field theory.

Exploring the Lorentz group O(3,1), its disconnected components, its defining invariant metric, and its fundamental representations in relativistic physics.

Building the language of Lie groups and their representations from the ground up — generators, structure constants, representations, Casimir operators, and the exponential map.

We derive the Faddeev–Popov identity using a discrete warm-up, insert it into the path integral, extract the gauge-fixed photon propagator, and ask: what other gauge-fixing terms are allowed?