e/Antisymmetrizer

Information
has gloss	eng: where the position vector ri of particle i is a vector in \mathbbR}^3 and σi takes on 2s+1 values, where s is the half-integral intrinsic spin of the fermion. For electrons s = 1/2 and σ can have two values ("spin-up": 1/2 and "spin-down": -1/2). It is assumed that the positions of the coordinates in the notation for Ψ have a well-defined meaning. For instance, the 2-fermion function function Ψ(1,2) will in general be not the same as Ψ(2,1). This implies that in general \Psi(1,2)- \Psi(2,1) \ne 0 and therefore we can define meaningfully a transposition operator \hatP}_ij} that interchanges the coordinates of particle i and j. In general this operator will not be equal to the identity operator (although in special cases it may be).
lexicalization	eng: antisymmetrizer
instance of	(noun) act of changing the lineal order of objects in a group permutation