### Tag: Time transformations

How Hamiltonians vary under coordinate changes

## How Hamiltonians vary under coordinate changes

TL;DR – Hamiltonians are not invariant: they change as the time component of a covector (i.e. covariant component) in phase space. In the previous post we saw how momentum varies as covariant components and that keeps the Hamiltonian equations unchanged under coordinate transformations. We have also seen, though, that under coordinate transformations that mix time …