# Infinite product notation

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.

It's a constitution of a ket

Ssnow
Gold Member
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 kn0 is greater than zero". This also became a little more clear once I picked up Peskin and Schroeder, and looked at Ch9.2.

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.

Ssnow