What does the `|' represent in an infinite product notation?

[blankvin]

Hi,
In my QFT course, the professor writes an infinite product like this:

∏_{n | k n⁰ > 0} ∫...

My question is, what does the `|' in the subscript "n | k" representing? When I see `|', I think logical OR - obviously that is not it. Normally, if it's a sum over two indices, commas separate the indices - not sure if `|' in place of a comma is standard notation or not.

Any ideas?Thanks,
blankvin.

 

[Morten]

It's a constitution of a ket

 

[Ssnow]

In math when you write $n|k$ it means that exist $c$ such that $k=c\cdot n$, in other words is the product over all divisors of $k$ ..., I don't know otherwise ...

 

[blankvin]

Thinking back to my complex analysis course, I think the bar `|' represents "such that", or "where". So,

∏_{n | kn⁰>0}

can be read as "an infinite product over n, where k_n⁰ is greater than zero". This also became a little more clear once I picked up Peskin and Schroeder, and looked at Ch9.2.

 

[blankvin]

In math when you write $n|k$ it means that exist $c$ such that $k=c\cdot n$, in other words is the product over all divisors of $k$ ..., I don't know otherwise ...

Yes, that's it. See P&S, p.285-286: k is defined as a constant times n. This makes sense.Thanks,
blankvin.