$$x \in \mathbb{R}^n \mbox{ (independent variables)}$$ $$y \in \mathbb{R}^n \mbox{ (dependent variables)}$$
$$f=f(x,y)$$
It is said that $f$ is invariant, or absolute invariant iff
$$Xf=0,$$ where X is the infinitesimal transformation symbol/operator, corresponding to a one-parameter Lie group. Let $\varphi=\varphi(x,y)$ is relative invariant. Then
$$X\varphi = ?$$
Some say that $X\varphi=0$ when $\varphi=0$. This is confusing...
Can someone explain,
$$X\varphi = ?$$