The discussion centers on the quantization of fermions and the necessity of using anti-commutation relations due to the spin-statistics theorem. It is established that, in four dimensions, no alternative relations exist that are compatible with fermions. The spin-statistics theorem provides a definitive framework for understanding this limitation in quantum mechanics.
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In 4 dimensions, no. This is provable, and called the spin-statistics theorem: http://en.wikipedia.org/wiki/Spin-statistics_theoremkof9595995 said:Prescription of QM tells you to us commutation relation and when quantizing fermions it's problematic, then we use anti-commutation relation instead. But can't there be some other relation besides anti-commutation that is also compatible with fermions?