What determine whether the dynamical equations are tensor equations or vector equations? Newton's 2nd law which is central to Newtonian dynamics, is a vector equation 
$\sum\textbf{F}_{external}=m\textbf{a}$
Same with Maxwell's equations in the covariant form.
On the other hand, general relativity is governed by the tensor equation
$\displaystyle R_{\mu\nu}-\frac{1}{2}R~g_{\mu\nu} =\frac{8\pi G}{c^4} T_{\mu\nu}$
My questions are:


*

*Is there a deep reason why some dynamical equations are tensor (of
the 2nd rank) equations and others are vector equations? 

*Is Schrodinger equation a scalar equation?  

*Are there dynamical equations in physics which are tensor equations of rank higher than
2? 

*Is there an upper bound on the highest rank a physics tensor
equation can have? from some physical argument may be?

 A: *

*The number of variables in a field state. This question is like "why electron mass is less than proton mass". Just because there is a choice.

*When discussing symmetry, it is better to discuss not Schroedinger equation but Klein-Gordon or Dirac equations which are scalar and spinor (1/2 rank tensor) equations. Schroedinger equation is a nonrelativistic limit of a second with spin neglected. It might give you a better picture than just a statement that it is scalar. Because technically it is not invariant.

*In solid state spin 5/2 is a normal thing. Half filled d-shells of some metals behave as they are spin 5/2 particles "under normal conditions" (until you are interested in a energy range where the system starts to feel its composite nature). Probably, there are situations where you have higher momenta which are better to treat effectively as a whole, without going into details of their formation.

*So far, no elementary particles with spin >2 are known. Consequently, equations for those particles have rank less than 2. There is no upper bound.

