- #1

- 45

- 0

**Question**

In index notation, can you have more than two occurances of the same index in the same term? Let me provide and example:

Let's say I have a two index tensor, [itex]M{\alpha \beta}[/itex], and I contract it with itself:

[tex]M_{\alpha \beta} M^{\alpha \beta}[/tex]

Then let's say I wish to operate on this product with some sort of two index operator, [itex]\chi_{\alpha \beta}[/itex]. Is it "legal" to write,

[tex]\chi_{\alpha \beta}[M_{\alpha \beta} M^{\alpha \beta}][/tex]

or must I introduce new indices,

[tex]\chi_{\gamma \sigma}[M_{\alpha \beta} M^{\alpha \beta}][/tex]

and then use the metric tensor and delta function to clean things up? None of the primers I've read are particularly clear on this point.