Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Scalar product and isospace

  1. Mar 2, 2009 #1
    In some textbooks you can find that a term
    [tex] \vec{\tau} \cdot \vec{A}_{\mu} = \sum_{a=1}^{3} \tau_{a} \, A_{\mu}^{a} [/tex]
    is called scalar product in isospace (where the tau's denotes the Pauli matrices and [tex]A_{\mu}^{a}[/tex] is a four-vector). But how can one call this "scalar" product. The product is a matrix and not a scalar. And the usual definition of a scalar product requires that the product has to be a scalar.

    Or take another example: [tex] \gamma^{\mu} \, A_{\mu} [/tex] is called a scalar product of four-vectors in space-time. It is confusing. Could anyone explain that to me? Do we really have a scalar product (in a strict mathematical sense) or is it just a convention done by physicists?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Scalar product and isospace
  1. Scalar field (Replies: 1)

Loading...