All Questions
8
questions
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Calculation of one-loop diagram in $\phi^4$ theory
In Folland's book Quantum Field Theory, page 207, he gives the value of the amputated one-loop $\phi^4$ diagram as
$$I(p) = \frac{(-i\lambda)^2}{2} \int \frac{-i}{-q^2 + m^2 - i\epsilon} \cdot \frac{-...
- 3,350
1
vote
0
answers
48
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Why we can Wick rotate momentum axis for correlation function?
In QFT writtern by Peskin and Schroeder, in page 293, PS wick rotate both time axis and momentum axis of correlation function of Klein-Gordon field, ie
$$D_F=<0|T\phi(x_1)\phi(x_2)|0>=\int\frac{...
- 326
2
votes
1
answer
139
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Do we wick rotate momentum axis on correlation function?
In QFT written by Peskin and Schroeder, it is discussed how correlation function is evaluated in Euclidean space, on page 292 to 293,
In (9.48)
$$<\phi (x_{E1})\phi(x_{E2})>=\int \frac{d^4k_E}{(...
- 326
1
vote
1
answer
76
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Performing Wick rotation under conjugation
See the formulas (95) and (96) of this notes https://arxiv.org/abs/1602.07982. When one try to perform the Wick rotation $t=-i\tau$ to the field in Minkowski/Lorentzian spacetime
$$\mathcal{O}_L(t, \...
- 161
4
votes
3
answers
901
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Wick rotation in Peskin and Schroeder's QFT
I know there are many similar analysis about this topic, like here, here, many of them are answered by Qmechanic, excellent answer!
I have checked most of these posts, but I still don't clearly ...
- 1,421
3
votes
0
answers
153
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Green Function in Euclidean space time
My question based on Ashok Das's "Finite Temperature Field Theory", page 12-13.
The book assume that in bosonic Klein-Gordon theory, zero temperature Green function satisfies (metric in ...
- 1,421
5
votes
1
answer
1k
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Different versions of Schwinger parameterization
One common used trick when calculating loop integral is Schwinger parameterization. And I have seen two versions among wiki, arxiv and lecture notes.
$$\frac{1}{A}=\int_0^{\infty} \mathrm{d}t \ e^{-tA}...
- 53
5
votes
1
answer
874
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Convert propagators from Euclidean to Minkowski spacetime
I'm looking for a rule to "convert" the propagators of a quantum field theory formulated in Euclidean spacetime into those of the same theory but in Minkowski spacetime (with the $\operatorname{diag}(-...
- 660