# Direct Product

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

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

Like O(3) ^ direct product blah

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 :)

Meir Achuz
Homework Helper
Gold Member
t is defined either by a Taylor expansion or by an eigenfunction expansion.

George Jones
Staff Emeritus
Gold Member
When the direct product is in the exponent of some variable, how is it defined?

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.

You mean something like

$G^{\otimes}$

Something like that. What does it mean?

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George Jones
Staff Emeritus
Gold Member
Something like that. What does it mean?

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.

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

thanks