Tagged Questions
1
vote
2answers
114 views
$\langle B|A \rangle$ expressed in terms of the Partition Function
Say you have an electron departing from point A and reaching poing B after a time t.
According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
5
votes
1answer
71 views
Significance of Poles of Correlation Function in QFT
In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
2
votes
1answer
111 views
Product of VEVs vs. VEV of product
How can we prove the following cluster decomposition formula
$$\langle \phi_1 \phi_2 \rangle ~=~ \langle \phi_1 \rangle \langle \phi_2 \rangle,$$
where brackets denote vacuum expectation value (VEV) ...
3
votes
0answers
62 views
Contact Term and Schwinger Term
In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'.
When deriving the quantum equations of motion for time-ordered ...
5
votes
2answers
158 views
Correlation, Time Ordering, and Observables
In general, the product of two Hermitian operators $\phi$ will not be Hermitian, unless the two operators commute.
Question: is $X = T \phi(t_1) \phi(t_2)$ Hermitian? It doesn't seem to be if
$T ...
5
votes
2answers
220 views
Can scattering amplitudes be simplified with 1PI diagrams?
I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
3
votes
2answers
183 views
How do I define time-ordering for Wightman functions?
This is a follow-up question to What are Wightman fields/functions
Ok, so based on my reading, the field operators of a theory are understood to be operator-valued distributions, that is, to be ...
4
votes
1answer
207 views
What are Wightman fields/functions
Simple question: What are Wightman fields? What are Wightman functions?
What are their uses? For example can I use them in operator product expansions? How about in scattering theory?
7
votes
1answer
374 views
Correlation function which has branch cut in momentum space
When correlation function has branch cut in momentum space,
how to find correlation in coordinate space?
For example
$$ \tilde {G}(\omega) = \frac{2i}{\omega+(\omega^2-\nu^2)^{1/2}}$$
How to get the ...
2
votes
0answers
360 views
How to prove Wick's Theorem (Zee's eq. I.2 (16)) via Gaussian integration?
I'm working through Zee's QFT in a Nutshell but there's an integral [I.2 (16)] I couldn't quite derive.
The problem is to find
$$\langle x_i x_j ... x_k x_l\rangle=\frac{\int ... \int dx_1 ... dx_n ...
13
votes
2answers
65 views
Calculating correlation functions of exponentials of fields
In their book Condensed Matter Field Theory, Altland and Simons often use the following formula for calculating thermal expectation values of exponentials of a real field $\theta$:
$$ \langle ...
2
votes
2answers
250 views
Correlation functions in thermal field theory etc
Suppose I am studying a field theory at finite temperature or some black hole formation scenario from boundary theory perspective in the sense of AdS/CFT. How is it possible to gain information about ...
