Understanding Zwiebach's Commutator Demands in 12.6 - Google Books

  • Thread starter ehrenfest
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Your Name]In summary, Zwiebach's approach in 12.6 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 and this is a fundamental concept in the theory. Zwiebach is using the fact that the creation and annihilation operators for bosonic and fermionic fields do not commute with each other, and 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. This is a well-established fact in quantum field theory and is not something that Zwiebach is arbitrarily choosing.
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ehrenfest
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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

 
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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.
 

FAQ: Understanding Zwiebach's Commutator Demands in 12.6 - Google Books

What is the significance of Zwiebach's Commutator Demands in 12.6?

Zwiebach's Commutator Demands in 12.6 is a mathematical concept proposed by physicist Barton Zwiebach in his book "A First Course in String Theory". It is a set of equations that describe the fundamental properties of strings and their interactions.

How does Zwiebach's Commutator Demands in 12.6 relate to string theory?

Zwiebach's Commutator Demands in 12.6 is a critical component of string theory, a theoretical framework that attempts to explain the fundamental structure of the universe. The equations describe how strings interact with each other and with the fabric of spacetime.

What is the purpose of studying Zwiebach's Commutator Demands in 12.6?

By understanding Zwiebach's Commutator Demands in 12.6, scientists hope to gain a deeper understanding of the fundamental building blocks of the universe and how they interact. This can lead to potential breakthroughs in our understanding of gravity, quantum mechanics, and the nature of space and time.

Are Zwiebach's Commutator Demands in 12.6 experimentally proven?

While there is strong theoretical support for Zwiebach's Commutator Demands in 12.6, they have not yet been experimentally proven. This is because the energy required to create and observe strings is currently beyond our technological capabilities.

How can Zwiebach's Commutator Demands in 12.6 impact other areas of science?

Zwiebach's Commutator Demands in 12.6 has the potential to impact a wide range of scientific fields, including cosmology, particle physics, and quantum gravity. It may also have practical applications in areas such as computing and material science.

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