Levi-Civita Contraction Meaning: Undergrad Research

[cmcraes]

Hi all, I'm doing undergraduate research this summer, and a few times I've been told to calculate a term with the following form: ∈^abcdp_aq_bk_cs_d, where p,q,k and s are four vectors (four-momentum, spin, etc). Now I know this ends up calculating exactly like a 4x4 determinant, I'm just not quite sure what its the determinant of (A matrix/tensor composed of these four vectors, I guess?), and what physical significance this quantity/determinant has.

Any and all insight is appreciated! (If it helps, I'm working on particles scattering problems)

 

[robphy]

What would you say for the two and three dimensional analogues of this problem?

In 3 dimensions, this might be represented by $\vec A\cdot(\vec B \times \vec C)$.