Personal website and Blogs
A path-integral and diagrammatic proof that any correlation function of an odd number of photon fields vanishes exactly — the photon is C-odd, the vacuum is C-even, and QED conserves C — plus the three places the proof most often goes wrong.
Spending Furry's theorem: no photon tadpole, no three-photon vertex, why Euler–Heisenberg has only even powers of F, whole classes of Feynman diagrams deleted for free, why light doesn't scatter off light until fourth order, and where the theorem breaks near a magnetar.
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?
Why you can't just write down the path integral for a gauge theory and call it a day — the operator you can't invert, the orbits you can't avoid, and the geometric picture that makes gauge fixing click.
Decomposing the fluctuations of massive vectors and massless 2-forms to determine their physical degrees of freedom and observational signatures.
Applying the cosmological principle to massive vectors and massless 2-forms to see if they can drive the expansion of the Universe.
A deep dive into gauge symmetry, equations of motion, constraints, and degrees of freedom for massive vectors and massless 2-forms.
An introduction to using higher-rank tensor fields like vectors and 2-forms as dark energy candidates, going beyond the scalar field quintessence.
Tutorial notes for the M.Sc. Cosmology core course at Heidelberg University — covers GR basics, FLRW cosmology, perturbation theory, and inflation.
Checking if Bose-Einstein Condensation can occur in 1D and 2D for free particles using periodic boundary conditions — and why the density of states is the key.
Do's and don'ts for surviving IPSP Leipzig — weekly assignments strategy, TP1 pitfalls, avoiding the course-failure loop, part-time jobs, and mental health.
A curated reading list for Classical Mechanics, featuring authoritative textbooks and resources used in leading physics programs worldwide.
Deriving the Mandelstam variables s, t, u for e+e- → μ+μ- scattering in the center-of-mass frame — from kinematics to Lorentz-invariant cross sections.
Deriving the virial expansion for a classical gas of hard spheres — from the Mayer f-function to excluded volume and higher-order corrections.
Tutorial notes for the M.Sc. Advanced QFT specialization course at Heidelberg — renormalization, Faddeev-Popov gauge fixing, and beyond.
A curated reading list for Cosmology, featuring authoritative textbooks and resources used in leading physics programs worldwide.
A practical guide to applying for Physics Ph.D. programs in Canada and Germany — where to look, how to contact supervisors, and how to prepare your documents.
When [A, B] = c is a constant, a slick ODE trick unlocks three powerful operator identities used throughout quantum mechanics.
Exploring how the quantum mechanical correlation function C(t) relates to the classical limit of a Gaussian state with width σ_ω.
Pure states, mixtures, ensemble averages, cyclic trace, and the von Neumann equation — all the core properties of the density operator worked out explicitly.
Deriving the electron neutrino survival probability from scratch using two bases, a rotation angle, and time evolution — plus why oscillations prove neutrinos have mass.
We decompose L·S using ladder operators and write the spin-orbit Hamiltonian explicitly as a 2×2 matrix in the Sz eigenbasis.
Given a general spin-1/2 state, we calculate the probabilities of measuring positive spin along y and z, and verify with known eigenstates.
How to prepare for IPSP Leipzig — math and physics foundations to build before arrival, why survival is harder than admission, and the German university model.
Deriving the explicit matrix form of the time-reversal operator for a spin-1/2 particle by expanding the exponential, and proving the famous result Θ² = −1 for fermions.
Using angular momentum conservation to constrain the final state of a particle decay, enumerating possible states, determining parity, and extracting spin measurement probabilities from Clebsch-Gordan coefficients.
Working through a discrete rotation group, its subgroups, eigenvalues of symmetry operators, non-commutativity of rotations and reflections, and using symmetry to identify vanishing matrix elements.
Deriving the transfer matrix connecting incoming and outgoing WKB amplitudes across a general potential barrier, and extracting the tunneling transmission coefficient.
Deriving the explicit matrix form and normalization of the spin eigenstates |n; +⟩ for a general unit vector n̂ defined by spherical angles θ and φ.
Tips and insights to ace the Heidelberg M.Sc. Physics interview — preparation strategy, common questions, and advice from experience.
A curated reading list for Quantum Field Theory, featuring authoritative textbooks and resources used in leading physics programs worldwide.
A deep dive into why "Hermitian" operators aren’t always self-adjoint, and why this matters for the momentum operator in quantum mechanics.
How to apply to IPSP Leipzig as an international student — HEQ requirements, Studienkolleg, JEE-Advanced eligibility, and the Uni-assist application process.
Tutorial notes for the M.Sc. General Relativity core course at Heidelberg University — Special Relativity, geodesics, curvature, and gravitational physics.
Electrodynamics literature recommendations
A detailed look at the directed polymer on a square lattice, counting microstates and calculating typical deflection using the partition function.
Tutorial notes for Theoretical Physics III — Classical Mechanics II, Special Relativity, and Classical Field Theory. Includes student-recorded video links.