31. The antisymmetric nature of the cross product can be recast into a tensorial form as follows. 32. Nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in spacetime. 33. So the pseudovector "'a "'can be written as an antisymmetric tensor. 34. To do so for fermions, for example, the antisymmetrizer builds such a completely antisymmetric state. 35. Is it antisymmetric by chance ? talk ) 19 : 17, 7 May 2014 ( UTC) 36. Some authors require \ leq to also be antisymmetric , so that the relation is a partial order. 37. The symmetric combination gives the ground state while the antisymmetric combination gives the first excited state as shown. 38. Neutrons are fermions and so obey Fermi Dirac statistics, which implies that the final state is antisymmetric . 39. The number of independent components of an antisymmetric tensor is given by entries of Pascal's triangle. 40. A given electronic \ & vibrational wavefunction will either be symmetric or antisymmetric with respect to this rotation.
