Some questions about commutation relation

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The discussion centers on the quantization of fields through the definition of commutation relations, highlighting their fundamental role in quantum mechanics. The distinction between commutation and anti-commutation is emphasized, with symmetry being the key factor. The forum participants recommend exploring Dirac's "Principles of Quantum Mechanics" for a deeper understanding of these concepts. Additionally, the relationship between classical Poisson brackets and quantum commutators is established, specifically that the Poisson bracket corresponds to the commutator divided by iħ.

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I don't understand why we quantize the field by defining the commutation relation.What's that mean?And what's the difference between the commutation and anticommtation?
 
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Welcome to PF.
We quantize a field by the commutation relation because of the definition of the field.
Them's the rules.

The difference between commutation and anti-commutation is symmetry.
Have a go seeing what happens if you try to quantize a field by the anti-commutator.
 
Its one way to quantize a system.

If you can get a hold of Dirac's - Principles Of Quantum Machanics he uses that spproach.

Basically it turns out if you assume the algebraic properties of the classical Poisson Bracket still applies in QM you end up with the Poisson Bracket is the same as the commutator divided by i hbar:
http://bolvan.ph.utexas.edu/~vadim/classes/2013s/brackets.pdf

Thanks
Bill
 

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