1. Klein-Gordon Equation The Klein-Gordon equation is a relativistic wave equation, related to the Schrödinger equation. It is second order in space and time and manifestly Lorentz covariant. It is a quantized version of the relativistic energy–momentum relation. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. The […]

## Backpropagation Algorithm

In the gradient decent learning process, we adjust the weights and biases to decrease the cost function. Backpropagation algorithm is used to find out the gradient of the cost function.

## Linear Response Theory

A small perturbation act on a system in equilibrium may produce an effect related to this external field, which can be treat as a linear response up to first order approximation.

## Tensor Analysis in Special Relativity

1. Vector analysis in spetial relativity A vector in an inertial frame can be written as (1) In another inertial frame which moving in the drirection with vecocity (2)

## Feynman Diagrams

In Coordinate Space The Green’s function of a fermion can be written as the sum of all connected diagrams

## Wick’s Theorem

Wick’s theorem is a way to reduce a time-ordered operator into the sum of normal-ordered operator and various contractions. Then, where is the time-ordered operator from? Why we need this reduction?

## Quantum Pictures

This note gives a comparison on the three quantum pictures. Also, the Dyson series are introduced with the help of time-ordering operators.

## From Denver To Seattle

Preface, July 21, Houston There’s no windows in our lab. Daylight passes without any signs left. Sometimes, I knew it’s pouring only when I stepped out this building. Or sometimes, the road was already dry, but the flowers under the crape myrtle trees told me a rain had just past. Eyesight began to drop again. […]

## Notes on Regression Analysis

1. Regression Analysis Regression analysis is a statistical process for estimating the relationships between a dependent variable() and one or more independent variables(). That is, estimating the parameters (also called weights) in (1) based on some training examples . Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap […]