What is OpenClaw? It's a self-hosted personal AI assistant gateway - it not only runs on your own machine, but also connects Claude to any messaging platform (WhatsApp, Telegram, Slack, iMessage, Discord, etc.), and gives it tools (browser, canvas, memory, cron, sessions). Full Repo Hierarchy openclaw/├── src/ # Gateway source (82 dirs, 35 files)│ ├── … Continue reading Quick Study of OpenClaw Repo

Kaparthy's autoresearch is a scientific method encoded as agent instructions. The agent is a ML trainer/researcher running overnight experiments on a GPU - modifying train.py, running 5-minute training runs, logging results, keeping improvements, reverting failures. Both GSD and Autoresearch aims to have the agents to automatically get a complex coding task done, The elegance of … Continue reading Kaparthy’s Autoresearch Github

GSD(get the shit done) is an autonomous AI agent CLI that runs multi-phase software projects end-to-end. The tagline: "One command. Walk away. Come back to a built project." Its key innovation is Each task gets a fresh context window so the context doesn't degrade over a long run. It creates and maintains four files: state.md, … Continue reading Review of gsd-build/gsd-2

We hear perturbation in QFT a lot, but what is it? It's Perturbing the free (non-interacting) theory by turning on interactions. The Lagrangian density of two fields consist the free part and interaction part. The latter, full interacting theory is generally impossible to solve exactly. So Treat the interaction, i.e. the time evolution / amplitudes … Continue reading Perturbation in QFT

According to Born’s rule, the probability is obtained from the square of the wavefunction. More generally, this is written as the product of the complex conjugate of the wavefunction and the wavefunction itself, ψ∗ψor(𝜓ˉ𝜓)ψ ∗ ψ or( 𝜓 ˉ 𝜓 ) to ensure the probability density is real and non-negative. Now focus on the Dirac … Continue reading Need Dirac Adjoint to Describe 1/2 Spinor’s Lorentz Transformation

It's originally invented by Green to solve difficult PDE problems, let's reduce it to simple matrix form first Now let's solve a real, simple PDE problem: If we increase the number of grid points: The formula turns into Green's function A Green's function is literally the inverse of a differential operator, just like: A−1

In history, Dirac derived Dirac Equation by combining Quantum Mechanics and Special Relativity, led the equation, Later: Lagrangian is constructed to reproduce the equation In this post, Let’s derive the Dirac equation from the Dirac Lagrangian step-by-step using the Euler–Lagrange equation.

Noether's theorem states that For every continuous symmetry of the action, there is a corresponding conserved quantity. Continuous symmetry → a transformation that can be done smoothly, not discrete. Action → integral of the Lagrangian over time. SymmetryConserved quantityTime translation (Lagrangian doesn’t depend explicitly on time)EnergySpace translation (Lagrangian doesn’t depend on position)MomentumRotational symmetry (Lagrangian doesn’t … Continue reading Conservation of Charge

Classic Field Theory: Before quantization, understand classical fields. Topics: Action principle Euler–Lagrange equations Lagrangian density Noether's theorem Important fields: Maxwell's Equations Scalar field theory Vector fields Key idea:Fields are the fundamental objects, not particles. Relativistic Wave Equations: Next learn equations describing relativistic particles. Important equations: Klein–Gordon Equation (scalar particles) Dirac Equation (spin-½ particles) Key concepts: … Continue reading Roadmap to Learn Quantum Electrodynamics (QED)

Knowing Minkowski's invariance ( p^2 = m^2 ), we can then deduce the propagator in the Klein-Gordon equation, that is, scalar field, then pole of the propagator in Quantum Field Theory. This is one of the clever conceptual insights physicists discovered. The reasoning is: Fields have wave equations. Wave equations allow plane waves with p2=m2p^2=m^2. … Continue reading Physicists Identify Particles by Looking for Poles in Correlation Functions