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Infinite product notation

  1. Feb 13, 2016 #1
    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?

  2. jcsd
  3. Feb 13, 2016 #2
    It's a constitution of a ket
  4. Feb 13, 2016 #3


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    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 ...
  5. Feb 13, 2016 #4
    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.
  6. Feb 13, 2016 #5
    Yes, that's it. See P&S, p.285-286: k is defined as a constant times n. This makes sense.

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