Sunday, May 18, 2014

special relativity - Direct Product vs Tensor Product


I am confused in the notation on page 67 and page 70 a text (http://www-pnp.physics.ox.ac.uk/~tseng/teaching/b2/b2-lectures-2018.pdf), whether it's talking about a direct product or an outer product:




  1. On page 67, it mentioned that



    "you can take a direct product of two $j = 1/2$ representations"



    and build representations of higher j.





  2. On page 70, it mentioned



    "we can think of [the Lorentz Group] as the direct product $SU(2) \times SU(2)$."





In each of the above, does the author mean Direct Product or Tensor Product?




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