Zwiebach question with link to text

[ehrenfest]

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

 

[Jimmy Snyder]

This equation (10.33) is not derived it is just given, correct?

Yes.

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 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.

 

[nrqed]

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.