latex

latex

Production mathematical typesetting for arXiv preprints, academic papers, and web-rendered equations. Covers the full pipeline from mathematical intuition → LaTeX notation → rendered output, for both document (PDFLaTeX/XeTeX) and web (KaTeX/MathJax) targets.

Core Math Environments

% Inline math — use sparingly, only for simple symbols in prose
The energy $E = mc^2$ follows from special relativity.

% Display math — numbered equation
\begin{equation}
  \mathcal{L} = \bar{\psi}(i\gamma^\mu \partial_\mu - m)\psi
  \label{eq:dirac}
\end{equation}

% Unnumbered display
\[
  \hat{H}\psi = E\psi
\]

% Multi-line aligned (align not eqnarray)
\begin{align}
  \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
  \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0\varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}
  \label{eq:maxwell}
\end{align}

Common Physics Notation

% Quantum operators
\hat{a},\, \hat{a}^\dagger          % annihilation / creation
\langle \psi | \hat{O} | \phi \rangle  % Dirac bracket
\hbar\omega                           % reduced Planck × frequency

% Statistical mechanics
Z = \mathrm{Tr}\left[e^{-\beta \hat{H}}\right]
\langle O \rangle = -\frac{\partial \ln Z}{\partial \lambda}

% General relativity
g_{\mu\nu},\quad R_{\mu\nu} - \tfrac{1}{2}g_{\mu\nu}R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}

% Information / entropy
S = -\sum_i p_i \ln p_i
\mathcal{I}(\rho) = S(\rho \| \sigma) = \mathrm{Tr}[\rho(\ln\rho - \ln\sigma)]

KaTeX Web Rendering

KaTeX is the correct choice for web — faster than MathJax, same quality for standard notation.

// Lazy-load — only when math detected
let _katex = null
async function renderMath(container) {
  const spans = container.querySelectorAll('.math-block, .math-inline')
  if (!spans.length) return
  if (!_katex) _katex = (await import('https://esm.sh/[email protected]')).default
  spans.forEach(el => {
    el.innerHTML = _katex.renderToString(el.dataset.formula, {
      displayMode:  el.classList.contains('math-block'),
      throwOnError: false,
    })
  })
}