# Direct Product

1. Mar 10, 2010

### Nusc

When the direct product is in the exponent of some variable, how is it defined?

2. Mar 10, 2010

### haushofer

I would say that it's defined via the Taylor expansion. Can you give the explicit expression?

3. Mar 10, 2010

### Nusc

Like O(3) ^ direct product blah

4. Mar 10, 2010

### haushofer

You mean something like

$G^{\otimes}$
? I never saw such a thing, but I would then guess it's a notation for

$G \otimes G \otimes G \otimes \ldots \otimes G$

Does that make sense in your context? Otherwise you should give the exact expression in LaTeX :)

5. Mar 10, 2010

### clem

t is defined either by a Taylor expansion or by an eigenfunction expansion.

6. Mar 10, 2010

### George Jones

Staff Emeritus
There seems to be confusion in this thread (at least for me).

Please write down clearly, completely, and precisely what you mean, or give a reference to a text or paper which uses the notation that you want want clarified.

7. Mar 10, 2010

### Nusc

Something like that. What does it mean?

Last edited by a moderator: Mar 10, 2010
8. Mar 10, 2010

### George Jones

Staff Emeritus
Do you mean "something like" or "exactly like"? You have to be precise.

Do you mean

$$\overset{k}{\otimes}V?$$

This is standard notation for

$$V \otimes V \otimes \ldots \otimes V$$

with $V$ repeated $k$ times.

9. Mar 10, 2010

### Nusc

10. Mar 10, 2010

### xepma

It's the tensor product of N copies of rho.

11. Mar 10, 2010

thanks