Tagged Questions
0
votes
1answer
83 views
2
votes
1answer
94 views
Getting rid of double delta function in Feynman rules
[1]
A very simple example of feynman rule for scalar fields.
After computing the diagram i have got the following:
$$
-i(2\pi)^4g^2\int d^4q \frac{i}{q^2 -m^2c^2}\delta^{(4)}(p_1 - p_3 -q)
...
3
votes
2answers
140 views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
3
votes
0answers
110 views
Zeta regularization gone bad
This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
5
votes
0answers
116 views
Using $\frac{1}{A+i\epsilon} = PV\frac{1}{A}-i\pi\delta(A)$ in Feynman Integrals
Are the following operations O.K.? This is related to the Feynman parameter trick.
$$F:= \int_0^1 \mathrm{d}x\int_0^{1-x}\mathrm{d}y \frac{1}{f(x,y)+\mathrm{i}\epsilon}.$$ Now using
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2
votes
1answer
206 views
Crazy Dirac Deltas
I'm not expecting any rigor in the following and the answers...since we're dealing with Dirac deltas in the context of QFT.
Consider the integral
$$
\int d^4q\ \Theta(q_0)\Theta(p_{3,0}+q_0)\ ...
6
votes
1answer
280 views
Loop integral using Feynman's trick
I am trying to show for the one-loop integral with three propagators with different internal masses $m_1$, $m_2$, $m_3$, and all off-shell external momenta $p_1$, $p_2$, $p_3$ the following formula ...
1
vote
1answer
150 views
Integral in Peskin and Schroeder
I'm having a bit of a slow day, and can't see how to do the following integral in Peskin and Schroeder (page 107 for anyone with the book). We've derived in the centre of mass frame the integral over ...
5
votes
0answers
201 views
Gaussian Integrals : Functional determinant expressed as a trace
Be $A_{ij}$ a symmetric matrix. Then I can easily write
$$
\int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx=
\sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
4
votes
1answer
308 views
A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)
I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
0
votes
0answers
160 views
Why does this integral come out imaginary?
Im working through Zee and I'm having a little trouble with some integrals. I'm trying to reproduce the analogue of the inverse square law for a 2+1 D universe and I figured I could start with the ...
3
votes
1answer
204 views
Spinor integration
I am learning on-shell methods for one loop integrals from this paper: Loop amplitudes in gauge theory: modern analytic approaches by Britto. Starting with formula (18) spinor integration is ...
