Is there a good list of all standard well known operators ? I found a list on wiki, but even many well known operators where not in the list, and I am wondering about operator symbols for some operators that I not are aware of is standardized or not

We have the well known d'Alembert operator. \(\Box=\frac{\partial^2}{\partial t^2}-\nabla^2\), is there also a standardized operator symbol for

\(\frac{\partial}{\partial t}-\nabla\)

? if not I could call it the heart operator for example \(\heartsuit=\frac{\partial}{\partial t}-\nabla\). An alternative would be \(\sqrt{\Box}\), but that I think would be very confusing and possibly misleading.

Second is there any standardized operator symbols for when time is three dimensional, have direction in space, I need something for

\(\nabla_t-\nabla=\frac{\partial}{\partial t_x}+\frac{\partial}{\partial t_y}+\frac{\partial}{\partial t_z}-\frac{\partial}{\partial x}-\frac{\partial}{\partial y}-\frac{\partial}{\partial z}\)

I could naturally just use \(\nabla_t-\nabla\), but if pages up and down then why not a more compact form. If not a standardized operator symbol for it already, then I was thinking of diamond symbol (is it used for something else in math?)

\(\Diamond=\nabla_t-\nabla=\frac{\partial}{\partial t_x}+\frac{\partial}{\partial t_y}+\frac{\partial}{\partial t_z}-\frac{\partial}{\partial x}-\frac{\partial}{\partial y}-\frac{\partial}{\partial z}\)

and "naturally"

\(\Diamond^2=\nabla_t^2-\nabla^2=\nabla_t\cdot\nabla_t-\nabla\cdot\nabla=\frac{\partial^2}{\partial t_x^2}+\frac{\partial^2}{\partial t_y^2}+\frac{\partial^2}{\partial t_z^2}-\frac{\partial^2}{\partial x^2}-\frac{\partial^2}{\partial y^2}-\frac{\partial^2}{\partial z^2}\)