Contraction of a tensor to produce scalar

[roberto85]

Homework Statement

Explain how it is possible to perform a contraction of the tensor
$T^{\beta \gamma}_{\delta \epsilon}$ in order to produce a scalar T

Homework Equations

The Attempt at a Solution

$$T^{\beta \gamma}_{\delta \epsilon}T_{\beta \gamma}^{\delta \epsilon}=T$$

Not sure if that is correct? Also not used the forums in a while so not sure I am using the LaTex correctly here.

 

[Ray Vickson]

Homework Statement

Explain how it is possible to perform a contraction of the tensor
$[T^{βγ}_{δǫ}]$ in order to produce a scalar T

Homework Equations

The Attempt at a Solution

$[T^{βγ}_{δǫ}] [T_{βγ}^{δǫ}] = T$

Not sure if that is correct? Also not used the forums in a while so not sure I am using the LaTex correctly here.[/B]

You can tell you are not using LaTeX properly, just by reading your own message. For in-line formulas and equations, use "# #" (with no space between the two #s) instead of "$" at the start and end of you object. Also: spell out the actual names of the Greek symbols, so that β is "\beta" (backslash + 'beta'), etc. For your first formula this gives $T^{\beta \gamma}_{\delta \omicron}$ (if the object "ǫ" is an $\omicron$---I could not figure it out).

For a displayed formula or equation, just use two $ signs (with no space between them) at the start and the end. That gives
$$T^{\beta \gamma}_{\delta \omicron}T_{\beta \gamma}^{\delta \omicron} = T$$
You can right-click on a formula or equation and ask for display as TeX, to see the commands used in the above two examples.

 

[roberto85]

You can tell you are not using LaTeX properly, just by reading your own message. For in-line formulas and equations, use "# #" (with no space between the two #s) instead of "$" at the start and end of you object. Also: spell out the actual names of the Greek symbols, so that β is "\beta" (backslash + 'beta'), etc. For your first formula this gives $T^{\beta \gamma}_{\delta \omicron}$ (if the object "ǫ" is an $\omicron$---I could not figure it out).

For a displayed formula or equation, just use two $ signs (with no space between them) at the start and the end. That gives
$$T^{\beta \gamma}_{\delta \omicron}T_{\beta \gamma}^{\delta \omicron} = T$$
You can right-click on a formula or equation and ask for display as TeX, to see the commands used in the above two examples.

Thanks Ray, i just edited the equation but can't see why its not displaying correctly? edit: i see now, sorry. Is that correct to say then that the covariant multiplied by the contravariant will reduce it to a scalar?