# Tagged Questions

Wick rotation substitutes an imaginary-number variable for a real-number time variable to map an expression or a problem in Minkowski space to one in Euclidean space which are easier to evaluate or solve. Use for all types of rigid analytic continuation maps.

47 views

### A problem in an integration related to Wick rotation

In quantum field theory, we often calculate some integrations using Wick rotation. In the following, I will carefully deal with an integration involving Wick rotation. In the end, I have found that I ...
58 views

### What is Hawking's, “No Boundary Conditions”? [closed]

In his "No Boundary Conditions", is Hawking stating that time is eternal? And what is the difference between Real Time and Imaginary Time? Is he saying there are two different arrows of time, and ...
137 views

### Quantum field theory: zero vs. finite temperature

I have recently been made aware of the concept of thermal field theory, in which the introductory statement for its motivation is that "ordinary" quantum field theory (QFT) is formulated at zero ...
96 views

### Sign of Wick rotation [closed]

Suppose you have the integral $$i \int^\infty_{-\infty} L_M(t) dt$$ and that $L_M$ contains two poles: when $t>0$ the pole lies above the t-axis and when $t<0$ the poles lies below the t-axis. ...
244 views

167 views

### The definition of the vacuum state of quantum field by path-integral

In the review Entanglement entropy of black holes by Sergey Solodukhin (arXiv:1104.3712, equation 13), I see a definition of vacuum state of quantum field by path integral over half of the total ...
186 views

### Two math methods apply the same loop integral lead different results! Why?

I tried to adopt the cut-off regulator to calculate a simple one-loop Feynman diagram in $\phi^4$-theory with two different math tricks. But in the end, I got two different results and was wondering ...
153 views

### Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
399 views

### Can temperature be a complex number?

Is it possible for a temperature to be a complex number? I want to say "no" but I can't be so sure. If it is possible I would like to know of an example. I found an interesting article which treats ...
784 views

448 views

### Complex numbers in quantum mechanics and in special relativity

Is there a physical relation between the use of complex numbers for the wavefunction in (non-relativistic) quantum mechanics and in special relativity (as formulated in the setting of Minkowski space)?...
74 views

### Geodesic approximation and Euclidean continuation

I recently read many articles in the context of the AdS/CFT correspondance in which the geodesic approximation is used (see for example section 3.5 here). The correlator between two boundary operators ...
330 views

### Is imaginary time a fifth dimension? [duplicate]

I've read that by introducing the concept of imaginary time, the dimension of time can be treated like a spatial dimension mathematically. Assuming, without imaginary time, one considers the universe ...
293 views

### Amplitude $\langle0|e^{-iHT}|0\rangle$ in A. Zee's QFT In A Nutshell

In his Quantum Field Theory In a Nutshell, in page 12, (Second Ed), A Zee says that conventionally, the amplitude $\langle0|e^{-iHT}|0\rangle$ is denoted by $Z$. In the next paragraph, he considers ...
190 views

### Why use a particular regularization for $\int_0^\infty \mathrm{d}x\,e^{i p x}$?

There are many badly defined integrals in physics. I want to discuss one of them which I see very often. $$\int_0^\infty \mathrm{d}x\,e^{i p x}$$ I have seen this integral in many physical problems. ...
182 views

### Root of $i$, which one to take?

The propagator of a free particle in 1d is $$K(x_b, t_b; x_a, t_a ) = \sqrt{\frac{m}{2\pi i \hbar (t_b-t_a)}} \exp \left [ \frac{i m (x_b-x_a)^2}{2 \hbar (t_b-t_a)} \quad \right ] .$$ It looks nice....
111 views

### Why is the value of the action integral in general relativity the same on all regions that are homologous?

In their famous paper Action integrals and partition functions in quantum gravity, Gibbons and Hawking argue that in order to avoid the singularity of a Schwarzschild black hole you can complexify ...
1k views

### Schrödinger equation derivation and Diffusion equation

I am aware of the debate on whether SchrÃ¶dinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for ...
304 views

### Imaginary time is to inverse temperature what imaginary entropy is to …?

The Wick-Rotation rotates imaginary time into inverse temperature (as can be seen from its "rotating" the SchrÃ¶dinger equation into the heat equation). Now since entropy is temperature's conjugate, I ...
188 views

### Feynman's $i\epsilon$ prescription in path integrals (Mark Srednicki)

On page 63 in M.S. book , why m^(-1) goes to (1-iÎµ)m^(-1) or m -> (1+iÎµ)m and how can i verify eq.(7.3)? On page 63 writes : Looking at $H(P,Q)= \frac{1}{2m} P^2 +\frac{1}{2}mÏ‰^2Q^2$ we see that ...
370 views

### LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free states,...