Some questions about commutation relation

[zbnju]

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?

 

[Simon Bridge]

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.

 

[bhobba]

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