Meaning of the word 'canonical' in physics I often encounter the term canonical in my study of physics. What does it mean? There is canonical momentum, canonical transformations and I have even heard the phrase 'proving something more canonically'. What does the word mean in each of these contexts?
 A: Sometimes it just means "official" or "standardized" or "really important", but usually it has the more precise meaning "relating to the Hamiltonian formulation of classical mechanics". The canonical momenta are usually first introduced in the Lagrangian framework, but they are the momenta that appear in the phase space of Hamiltonian mechanics. Canonical transformations are symmetries of that phase space that preserve the symplectic structure. Canonical perturbation theory is formulated within Hamiltonian mechanics. The canonical commutation relations are a quantized version of Poisson brackets (as per Dirac's quantization rule).
A: Even in physics, the term canonical requires a disambiguation for clarity. In the contexts you were citing, it means that it is a more general form. E.g. if you are dealing with momentum, then the canonical momentum refers to $p = p + q \bf{A}$, however, momentum in a Newtonian physics course would most certainly refer to $p=mv$, thus, a professor might call momentum canonical to clarify that he does not mean the more simple version, but the more general version.
For other uses of canonical, see Wikipedia's disambiguation below:
https://en.m.wikipedia.org/wiki/Canonical
Hope this clears up your answer!
