Pseudotensors for describing physical quantities

Question

I have been reading about tensors from Mathematical methods for Physics and Engineering, by K.F. Riley, M.P. Hobson and S.J. Bence. And there are a couple of things i am not getting. On page 949 (section 26.10, chapter 26), its stated "Vectors can be divided into two categories: polar vectors(position, velocity), which reverse direction under an active inversion of physical system through the origin, and axial vectors(such as angular momentum), which remain unchanged. It should be emphasized that at no point in this discussion have we used the concept of a pseudovector to describe a real physical quantity." Now, according to pseudovectors pseudovectors and axial vectors are equivalent terms. So, i am pretty confused to the statement made in the book. Also, in the next section (page 949, section 26.11), its stated that "Although pseudotensors are not themselves appropriate for the description of physical phenomenon, they are sometimes needed" But Magnetic field is a pseudotensor. I am relatively new to these topics. So can someone clear it up for me? Here is a link to the statements from the book(page 798 in this link) :Riley Hobson

Answer 1

The claim you quote is utter nonsense.

Pseudotensors (in the sense of quantities that do not change sign under reflection like ordinary tensors of the same rank, not in the sense of the pseudotensors in General Relativity) are perfectly appropriate for the description of physical phenomena. Some quantities genuinely are pseudotensors, such as e.g. angular momentum and the magnetic field, see also this answer of mine for a general explanation of pseudotensors and this answer for a closer look on angular momentum and magnetic fields.