Language and conventions

The same word or symbol can describe different objects in different QFT calculations. This chapter gives short definitions, a notation guide, and the convention choices used throughout QFT.org. It is a place to resolve a specific uncertainty before returning to a calculation or lesson.

Definitions, symbols, and conventions

If you need to…	Open…	What you will find
Distinguish a field, state, observable, or propagator	Glossary	Concise definitions and the distinctions that prevent common mistakes
Decode $D_F$, $Z[J]$, $\Gamma$, or $\beta$	Symbols and notation	A definition, dimensions where applicable, and cautions about reused letters
Compare two signs or normalizations	Conventions and normalizations	Metric, Fourier phase, source sign, gauge normalization, and explicit translations

Definitions answer what an object is. Conventions fix how it is represented. A minus sign can be a harmless convention change only if the dependent definitions change with it.

A propagator is more than a denominator

Suppose two sources both write a quantity with denominator $p^2-m^2$. Before identifying them, check whether the numerator contains $i$, how the poles are displaced, and whether the quantity is a vacuum correlator or a Green function normalized to a delta source. These choices distinguish time ordering from causal response.

For the site’s free scalar convention, $D_F$ denotes the time-ordered vacuum correlator, while $G_F=iD_F$ is the delta-normalized inverse of $\Box+m^2$. The propagator guide collects the equations and a direct normalization check. Scalar Propagators, Ordered Correlators, and Sources derives them from the mode expansion.

Moving between sources

Start by identifying the physical object: its state, ordering, dimension, and boundary conditions. Then compare the metric, Fourier phase, source coupling, and any factors absorbed into its name. Translate the whole set of dependent definitions and check an equation that fixes the normalization, such as the sourced field equation or an equal-time commutator.

The conventions page contains the reusable packages for this comparison. The formulas chapter states additional assumptions that are specific to individual calculations; they are not replacements for the global convention system.