Zwiebach question with link to text

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In summary: What does normalization mean in this context?It means that the norm (also called the length) of \phi_p is 1.By the "volume of space" factor V, does he really mean a Jacobian?No, it is just a numerical factor that is meant to cancel out somewhere down the line when a volume integral is performed. In fact, he points this out in the text just below equation (10.36) on page 173.Also for Quick Calculation 10.3, how can E_p possibly get in the numerator when it is in the denominator of phi_p?This is straightforward, so I don't want to spoil your fun in figuring it
  • #1
ehrenfest
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Homework Statement


http://books.google.com/books?id=Xm...nDQ&sig=Eqnkxjj7B9gc4-nig1fgUkk7AqQ#PPA172,M1
I am very confused about equation 10.33.

This equation is not derived it is just given, correct?

What does normalization mean in this context?

By the "volume of space" factor V, does he really mean a Jacobian?

Also for Quick Calculation 10.3, how can E_p possibly get in the numerator when it is in the denominator of phi_p?

Homework Equations


The Attempt at a Solution

 
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  • #2
ehrenfest said:
This equation (10.33) is not derived it is just given, correct?
Yes.

ehrenfest said:
What does normalization mean in this context?
It means that the norm (also called the length) of [itex]\phi_p[/itex] is 1.

ehrenfest said:
By the "volume of space" factor V, does he really mean a Jacobian?
No, it is just a numerical factor that is meant to cancel out somewhere down the line when a volume integral is performed. In fact, he points this out in the text just below equation (10.36) on page 173.

ehrenfest said:
Also for Quick Calculation 10.3, how can E_p possibly get in the numerator when it is in the denominator of phi_p?
This is straightforward, so I don't want to spoil your fun in figuring it out. Besides in the homework forum, I'm really only allowed to guide you, not tell you. So do as the author says and plug (10.33) into (10.7) [Note: actually, you had better plug it into (10.35) because even though they are meant to be the same, (10.7) has a typo in it or does in my copy of the book]. You will need to apply equation (2.65) page 24, to get the E factor correct.
 
  • #3
ehrenfest said:

Homework Statement


http://books.google.com/books?id=Xm...nDQ&sig=Eqnkxjj7B9gc4-nig1fgUkk7AqQ#PPA172,M1
I am very confused about equation 10.33.

This equation is not derived it is just given, correct?

Actually, this is simply the most general solution to the equation of motion for phi (eq 10.14). As he wrot, a plane wave solution is of the form 10.16 so a general solution is a linear combination as in 10.33. At this point, there is nothing about qft of particle physics stuff...it's just solving a diff eq. The V factor is convenient if one works in a "box" with peridoic boundary conditions. It's put there to cancel later on in the calculation.
 

1. What is the Zwiebach question?

The Zwiebach question is a fundamental question in the field of string theory that asks for a mathematical description of the early universe. It is named after physicist Barton Zwiebach who proposed the question in the late 1980s.

2. How is the Zwiebach question related to string theory?

The Zwiebach question is closely related to string theory as it seeks to understand the fundamental nature of the universe using the principles of string theory. It asks for a way to mathematically describe the universe in its earliest stages, which is a key aspect of string theory.

3. What makes the Zwiebach question difficult to answer?

The Zwiebach question is difficult to answer because it requires a deep understanding of both string theory and cosmology. It also involves complex mathematical concepts and requires a unification of different theories, making it a challenging problem to solve.

4. Has there been any progress in answering the Zwiebach question?

Yes, there has been some progress in addressing the Zwiebach question. Some researchers have proposed potential solutions, but there is still no consensus on a definitive answer. It remains an active area of research in theoretical physics.

5. Why is the Zwiebach question important?

The Zwiebach question is important because it seeks to understand the fundamental nature of the universe, which has been a central question in physics for centuries. It also has the potential to unify different theories and provide a deeper understanding of the laws governing the universe.

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