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:

On page 67, it mentioned that

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

and build representations of higher j.

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?

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?

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:

On page 67, it mentioned that "you can take a direct product of two j = 1/2 representations" and build representations of higher j.

On page 70, it mentioned "we can think of [the Lorentz Group] as the direct product SU(2) × SU(2)"

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

On page 67, it mentioned that

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

and build representations of higher j.

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?