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In $\S 7.5.$ On Connection between spin and statistics: Bogoliubov Shirkov conclude their discussion (about quantization with commutator or anticommutator) with:
The results obtained represent a particular case of the fundamental Pauli theorem that establishes the relationship between the transformation properties of the field and the way of quantizing it (the connection between spin and statistics):
Fields describing particles with integral spin are subject to Bose-Einstein quantization; fields
describing particles of half-integral spin are subject to Fermi-Dirac quantization.
| Fields describing particles with integral spin are subject to Bose-Einstein quantization; fields describing particles of half-integral spin are subject to Fermi-Dirac quantization. |
The Pauli theorem is applicable to fields of arbitrary (no matter how high) spin.
Our proof made use of symmetry under charge conjugation.
However other reasoning is possible.
Violation of connection between spin and statistics, established by Pauli theorem,
leads to a number of deep contradictions.
To learn more got to \(\S10.2\S10.3\) of N.N. Bogoliuobov and D. V, Shirkov, Theory of Quantized Fields, 3rd edn, John Wiley and Sons, NY (1980)
