I have often read about the fact that angular momentum vector is a pseudo vector, that is, an axial vector. According to what I remember pseudo vectors are those vectors that do not change their sign upon reflection. So if I have two vectors $\mathbf r$ and $\mathbf {\omega}$, these two vectors would gain a negative sign upon reflection and then a cross product of them will give me $\mathbf L$ and this will be a pseudo vector. Am I correct?


1 Answer 1


Under inversion momentum and position will change signs as you said and angular momentum vector $L=r\times p$ will be written as

$$L=(-1)^2r \times p$$

so it's a pseudovector but triple vector product will be a polar vector as you can verify easily $A=B\times (C\times D) \hspace{2mm},\hspace{2mm} -A=(-1)^3 B\times (C\times D)$.

  • $\begingroup$ So the initial and final vector $L$ are the same vectors under inversion, correct? $\endgroup$
    – Ruchi
    Commented Jan 24, 2021 at 11:49
  • $\begingroup$ that's correct. $\endgroup$
    – Monopole
    Commented Jan 24, 2021 at 12:21

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