All Questions
Tagged with quantum-field-theory wick-rotation
157
questions
3
votes
3
answers
594
views
Path integral at large time
From the path integral of a QFT:
$$Z=\int D\phi e^{-S[\phi]}$$
What is a nice argument to say that when we study the theory at large time $T$, this behaves as:
$$ Z \to e^{-TE_0} $$
where $E_0$ is the ...
- 411
1
vote
0
answers
63
views
Path integral without wick rotation [closed]
As far as i know path integrals are usually evaluated by wick rotation to imaginary time, then making imaginary time finite and periodic/anti-periodic (bosons/fermions) with period beta=1/T (inverse ...
- 377
1
vote
0
answers
71
views
Motivation behind reflection positivity
I have taken a look at this physicsSE question, Wikipedia, and this paper by Jaffe which go over reflection positivity. While they all nicely explain the definition behind reflection positivity and ...
- 3,350
1
vote
0
answers
142
views
How is Wick rotation an analytic continuation?
Wick rotation is formally described by the transformation
$$t \mapsto it.$$
In many place it is stated more rigorously as an analytic continuation into imaginary time. I understand why we do it but ...
- 3,350
2
votes
1
answer
174
views
Examples of Path integral $\neq$ Partition function?
Are there any systems we know of whose partition function is not simply Wick rotation of the path integral? Does anyone know of any examples?
- 1,190
0
votes
1
answer
92
views
How do I show that Thermal Field Theory works?
Of course it does work. What I'm asking is:
What is the easiest-to-understand, most direct example that shows that Thermal Field Theory is a predictive theory that actually describes how temperature ...
- 5,931
2
votes
0
answers
68
views
Wick rotation of CFT three-point function
Let $\langle O_1\cdots O_n\rangle$ be a Euclidean CFT$_d$ correlation function. I know that we can analytically continue to Lorentzian signature as follows. Let $x_i = (\tau_i,\mathbf{x}_i)\in\mathbb{...
- 36.4k
10
votes
1
answer
222
views
Wick Rotation vs Sokhotski-Plemeli Method to compute internal loop of Feynman correlators
When computing loop integrals in QFT, one often encounters integrals of the form
$$\int_{-\infty}^\infty\frac{dp^4}{(2\pi)^4}\frac{-i}{p^2+m^2-i\epsilon},$$ where we are in Minkowski space with metric ...
- 101
3
votes
1
answer
104
views
How can we use saddle point approximation for a bounce solution which is not even a strict local minimum of the Euclidean action?
In calculating the false vacuum decay, the main contribution to the imaginary energy part of the Euclidean path integral comes from the bounce solution. And we somehow apply saddle point approximation ...
- 619
5
votes
1
answer
168
views
Justification for Wick rotation for topological insulator
In Appendix B of the paper (1), the authors compute the second Chern number $C_2$ of a band structure by manipulating the ground- and excited-state projection operators $P_{\text{G}}(\mathbf{k})$ and $...
- 2,157
6
votes
1
answer
240
views
Validity condition for Wick rotation?
I'm reading page 193 of section 6.3 of the QFT textbook by Peskin and Schroeder. There are two integrals that we need to evaluate for the calculation in this section. (here, $\Delta>0$)
$$\int\frac{...
- 151
1
vote
0
answers
60
views
Is the Euclidean generating functional $Z_{E}[J]$ identified with original Minkowskian generating functional $Z[J]$?
In quantum field theory, it is common to perform wick rotation $t\rightarrow -i\tau$ and get Euclidean generating functional $Z_{E}[J]$. When I first studied QFT, I just saw this a magic trick to ...
- 81
2
votes
0
answers
22
views
Dimensional regularisation and Wick theorem [duplicate]
Consider an integral:
$$I^{ij}=\int\frac{d^d\textbf{p}}{(2\pi)^d}p^i p^j f(\textbf{p}^2).$$
How can we show that this is equal to:
$$I^{ij}=\frac{\delta^{ij}}{d}\int\frac{d^d\textbf{p}}{(2\pi)^d}\...
- 183
2
votes
1
answer
459
views
Temperature of quantum fields and periodicity
I have read this PSE post Finite Temperature Quantum Field Theory, saying that
In a QFT at finite temperature, we consider the Euclidean time to be periodic, i.e. we consider a theory on the manifold ...
- 3,982
0
votes
1
answer
151
views
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