What is the intuition behind Noether current $$J^{\mu}_N={\Pi}^{\mu}D{\phi}-W^{\mu}$$ where ${\Pi}^{\mu}$ is the generalized conjugate momentum and $W^{\mu}$ is just some arbitrary function of spacetime.
- $J^{\mu}_N$ is the Noether current.
- $D\phi$ is the change of the field $\phi$ with respect to some parameter $\lambda$.
- ${\Pi}^{\mu}$ is the generalized conjugate momentum.
- $W^{\mu}$ is some arbitrary funtion of spacetime.