What are some examples of mixed tensors in physics?

[quasar987]

Can anyone give me examples of mixed tensors that appear in physics? I'm looking for mixed specifically here: purely covariant or contravariant ones won't do.

 

[arkajad]

$$\delta^\mu_\nu$$

 

[quasar987]

tensors of a physical nature...

 

[arkajad]

$$\kappa^\mu_\nu=\kappa\,\delta^\mu_\nu$$

$\kappa$ - gravitational constant

 

[robphy]

Riemann Curvature $$R_{abc}{}^d$$ (whose trace gives the Ricci Tensor appearing in Einstein's Field Equation) and (maybe) Torsion $$T^a{}_{bc}$$.

 

[haushofer]

Perhaps not entirely "tensors", but spin 3/2 particles represented by

$$\psi_{\mu}^{\alpha}$$
where alpha is a spinorial index.

 

[arkajad]

Every operator in quantum mechanics is a mixed tensor. In a basis it is represented as a tensor $A^i_j$. For instance, if we want to stay in finite dimensions, a density matrix operator for spin 1/2.

For space, every 3-dimensional active rigid rotation is an operator. It can be considered as a tensor $R^i_j$.