A guide to Feynman diagrams in the many-body problem

[fluidistic]

I'm trying to go through Mattuck's book "A guide to Feynman diagrams in the many-body problem", the Dover's 2nd edition book.

I have read that apparently it has been criticized for being way too easy. I'm having an extremely hard time going through the 3rd chapter, let alone the 4th! I feel like it started as 1+1=2, then next page there are ##10^{23}## Feynman diagrams thrown in your face. The learning curve is steeper than a skyscraper.

Nevertheless, I created this thread to point out possible mistypes and errors of the book. And also for you people to help me out when I'm lost.

Here are my current comments:
Page 53, in the right hand side of expression 3.49, should ##(t-t')## be ##\delta(t-t')##? (I guess so, trivially).

Page 28:

(...) and consider just ##P(r_2,r_1)##; this is the probability that if the particle begins at ##r_2##, it will finish at ##r_2## regardless of the time

. Should it read "(...) the particle begins at ##r_1##(...)"? Again, I guess so, trivially.

(I do remember having spotted another typo, but I forgot where).

Now something more serious. Page 43, about the expressions that are after eq. 319.
Mattucks claims that ##H\approx m_0c^2+\frac{p^2}{2m_0}-\frac{p^4}{8m_0^3c^2}## and that if we define ##m_0=m+m_e##, one gets that ##H\approx (m+m_e)c^2 + \frac{p^2}{2m} - \frac{m_e}{(m_e+m)m}p^2 - \frac{p^4}{8(m+m_2)^3c^2}##. But I do not get that at all! I get that this would be true if some of the masses were either 0 or infinity, but this is certainly not what Mattuck had in mind.
Had Mattuck made a mistake here? If so, how can we fix it so that his assertion holds: namely that this latter Hamiltonian has the form of eq. 319 (except for the unimportant constant)?

 

[dRic2]

I have no clue of what you are talking about ahahahah (I'm just an engineer )

Anyway I noticed the following:

1)

if we define ##m=m+m_e##

Shouldn't it be ##m_0 = m + m_e##? just a typo but, you know, to be sure...

2) I think it is missing a "2" in the denominator of

## - \frac {m_e} {(m_e + m)m} p^2##

Because otherwise the identity comes from:

$$ + \frac {p^2} {2m} - \frac {m_e} { \mathbf 2 (m_e + m)m} p^2 = \frac {p^2(m_e + m) - m_ep^2}{2 (m_e + m)m} = \frac {p^2m}{2 (m_e + m)m} = \frac {p^2}{2 (m_e + m)} = \frac {p^2} {2m_0}$$

 

[fluidistic]

I have no clue of what you are talking about ahahahah (I'm just an engineer )

Anyway I noticed the following:

1)
Shouldn't it be ##m_0 = m + m_e##? just a typo but, you know, to be sure...

2) I think it is missing a "2" in the denominator ofBecause otherwise the identity comes from:

$$ + \frac {p^2} {2m} - \frac {m_e} { \mathbf 2 (m_e + m)m} p^2 = \frac {p^2(m_e + m) - m_ep^2}{2 (m_e + m)m} = \frac {p^2m}{2 (m_e + m)m} = \frac {p^2}{2 (m_e + m)} = \frac {p^2} {2m_0}$$

Yes for 1), I've edited my post.
Thanks a lot for 2), I hadn't figured that out! That makes sense...

I now have a general question. If we consider diagrams such as the one in p.54, why are some ##k_1## and ##k_2## labels omitted? Would it be wrong to place the labels on every single term of the infinite series? Why is there a ##k_1## label but no ##k_2## label on the 1st term? Is it a lazy/sloppy omission or is there anything deep I'm missing?