- #1
thatboi
- 130
- 20
Hi all,
I am having trouble understanding the argument below equation (3.5) in https://arxiv.org/pdf/cond-mat/9605145.pdf where they claim that "Upon antisymmetrization, however, a term with ##k## factors of ##(z_{i}-z_{j})## would have to antisymmetrize ##2k## variables with a polynomial that is linear in each", which is impossible.
However, I thought that even for something like ##(z_{1}-z_{2})(z_{3}-z_{4})##, I can antisymmetrize this expression by just using the definition of the antisymmetrizer, i.e I sum over all permutations of the indices ##(1,2,3,4)## and include ##\pm## signs as appropriate depending on how many times an index has been shifted. So why does the paper claim that the antisymmetrizer vanishes?
Thanks.
I am having trouble understanding the argument below equation (3.5) in https://arxiv.org/pdf/cond-mat/9605145.pdf where they claim that "Upon antisymmetrization, however, a term with ##k## factors of ##(z_{i}-z_{j})## would have to antisymmetrize ##2k## variables with a polynomial that is linear in each", which is impossible.
However, I thought that even for something like ##(z_{1}-z_{2})(z_{3}-z_{4})##, I can antisymmetrize this expression by just using the definition of the antisymmetrizer, i.e I sum over all permutations of the indices ##(1,2,3,4)## and include ##\pm## signs as appropriate depending on how many times an index has been shifted. So why does the paper claim that the antisymmetrizer vanishes?
Thanks.