For a deep understanding of Green's function, we need to refresh knowledge on probability, starting from two variables x1 and x2: Given the coupling effect here due to the matrix A is not 1, 0 and 0, 1, large values of x1,x2x_1,x_2x1​,x2​ are strongly suppressed. This coupling is exactly why correlations appear, and those correlations … Continue reading Green’s Function in QFT 0

It's fascinating to see that Green's function, which I once thought was merely a trick to solve challenging PDE problems, is inherently present in QFT, especially when a genius like Richard Feynman attempts to develop the algebra needed to compute field interactions. In this blog, I want to lay down the fundamentals and then progress … Continue reading Green’s Function in QFT 1: Basics

Deriving this Lagrangian in scalar field: the key is to Replace particle with a field. If the field interacts with itself, the simplest form, the Lagrangian is

Physics is described by the Lagrangian: L = T - V where T is the kinetic energy and V is the potential energy. For fields,

Imagine a particle moving from point A to point B. In quantum mechanics, it doesn’t just take a single path — it explores all possible paths. Each path has a complex amplitude (or wave function) with a phase determined by the action along that path. The sum of all these amplitudes determines the probability for … Continue reading Feynman Paths to Feynman Diagrams: A Journey Through Quantum Arrows

When we think about derivatives, most of us picture that familiar dydx\frac{dy}{dx}dxdy​ symbol, a slope on a graph, or a rate of change in a physics problem. But let's step back. Strip away the numbers and the curves. What really is a derivative? It’s an operator. Or, if you like to think in linear algebra … Continue reading Derivative: Operator, Matrix Transformer, and Bridge to Quantization

The quantum world is bizarre; properties such as position and speed cannot be measured using real numbers. Instead, they require an operator, more specifically, a Hermitian operator, for measurement. when we talk about measuring, we mean to get the probability of a unique quantum state and expected value of a generic quantum wave/particle. The premise … Continue reading Deep Understanding of Operator in QM

What I learned through long, lonely stretches of study is simple: never set a goal to impress others. The moment the target is external, the work becomes fragile. Motivation fluctuates with attention. Validation becomes the fuel. And fuel like that runs out. When I shifted the goal inward—to improve, to understand, to satisfy my own … Continue reading Satisfy Your Own Standard

Most of what we call understanding is just fast pattern recognition. Intuition feels deep because it is effortless. But when it comes to reality at its foundations, intuition consistently fails. Common sense said heavier objects fall faster. Galileo Galilei showed otherwise. Space and time feel absolute; Albert Einstein proved they are not. None of these … Continue reading Against Intuition

Experiments showed strange asymmetries in weak decays, beta decays, but no one related this to parity violation. Tsung-Dao Lee and Chen-Ning Yang carefully reviewed all experiments. They concluded: There was no experimental proof that weak interactions conserve parity. They proposed: Do an experiment in beta decay with polarized nuclei. If parity is conserved → electron … Continue reading Nature Prefers One Handedness