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,
    })
  })
}

/* Dark-theme KaTeX overrides */
.katex { color: #e8ebf2; font-size: 1.05em; }
.math-block {
  display: block; text-align: center;
  padding: 14px; margin: 16px 0;
  background: rgba(139,92,246,0.06);
  border: 1px solid rgba(139,92,246,0.18);
  border-radius: 10px; overflow-x: auto;
}

arXiv Submission Formatting

\documentclass[12pt]{article}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{hyperref}
\usepackage[numbers]{natbib}

% Required by arXiv: include all source files + .bbl (not .bib)
% Max upload: 50 MB. Figures as EPS/PDF, not PNG/JPEG for vector content.

\begin{document}
\title{Orbital Routing via Physical Analogy}
\author{Author One \and Author Two}
\date{\today}
\maketitle

\begin{abstract}
We present...
\end{abstract}

\section{Introduction}
...

\bibliographystyle{unsrtnat}
\bibliography{refs}   % compile refs.bbl before submission
\end{document}

Symbol Reference

Checklist

• [ ] Use align not eqnarray (avoids spacing bugs)
• [ ] Label every numbered equation — \label{eq:name}
• [ ] \left(, \right) for auto-sizing delimiters
• [ ] \mathrm{} for upright text in math (units, operators): $\mathrm{d}x$
• [ ] \text{} for words inside equations: $x \text{ if } x > 0$
• [ ] Never use $$...$$ in LaTeX documents — use \[...\] or equation env
• [ ] KaTeX supports \ce{} for chemistry via mhchem extension

_Last reviewed: 2026-05-14 — automated polish pass per issue #62._