Understanding Zwiebach's Commutator Demands in 12.6 - Google Books

[ehrenfest]

zwiebach page 207 with link to text

Homework Statement

I just do not understand why Zwiebach can just "demand" that operators fail to commute like he does in 12.6 and just set commutators equal to what he wants? Why does he not have to prove 12.6?
http://books.google.com/books?id=Xm...kCA&sig=Eqnkxjj7B9gc4-nig1fgUkk7AqQ#PPA207,M1

Homework Equations

The Attempt at a Solution

 

[Jhero]

I understand your confusion about Zwiebach's approach in 12.6. It may seem like he is just imposing his desired commutators without any justification. However, in quantum field theory, operators do not always commute with each other. This is a fundamental concept in the theory and is not something that can be proven or derived from first principles. It is simply a property that is observed in nature and is incorporated into the theory.

In this particular case, Zwiebach is using the fact that the creation and annihilation operators for bosonic and fermionic fields do not commute with each other. This is a well-established fact in quantum field theory and is not something that Zwiebach is arbitrarily choosing. By setting the commutators to the desired values, he is ensuring that the operators behave in a way that is consistent with our understanding of bosonic and fermionic fields.

I hope this explanation helps to clarify the issue. If you have any further questions, please do not hesitate to ask.