Sign convention

Annoyingly often in physics, some textbooks and articles use definitions for certain quantities with the opposite sign from other textbook/articles. This lack of standardization is a frequent source of confusion, misunderstandings and even outright errors. A choice of signs in the definition is called a sign convention. Sometimes, this term is used more sloppily to include factors of <math>i<math> and 2<math> \ \pi<math>.

A noncomprehensive list of sign conventions:

• In relativity, the metric signature could either be +--- or -+++.
• The choice of <math>\pm<math> in the Dirac equation.
• The sign of the Faraday 2-form in gauge theories.
• The sign of work in the first law of thermodynamics.
• Time dependence of an electromagnetic wave:
  • <math>\exp(i\omega t)<math> (mainly used by physicists)
  • <math>\exp(-j\omega t)<math> (mainly used by engineers)

It is often considered good form to explicitly state which sign convention you are using at the beginning of every article/book.

Warning: Since this encyclopedia is written by hundreds of different mathematicians/physicists, there is absolutely no guarantee of consistency in sign conventions here. Proceed at your own peril.