All Questions
Tagged with path-integralquantum-field-theory
914 questions
0votes
0answers
32views
Zeta-function regularization of constant product
I want to calculate a functional determinant coming from a Gaussian path integral with operator Matrix $M$. The determinant is given by the product over the eigenvalues according to $$\text{det}(M) = \...
2votes
1answer
151views
Beginner friendly materials for functional method in QFT
When I ask questions on this site regarding Feynman diagram, I see a lot of answers using functional method in QFT (e.g. this post and this post). However, they seems quite confusing to me because I'...
2votes
0answers
45views
Infrared zeromodes and the physical status of infinite-wavelength photons in quantum field theory
In quantum field theory, photons are described as quantized excitations of the electromagnetic field, with energy given by $E = ℏω = hc/λ$. In the infrared (IR) limit, where the wavelength $λ$ tends ...
- 21
2votes
2answers
702views
Why are free quantum fields said to be Gaussian?
This is perhaps a very elementary question, but it's something I was thinking about today and couldn't come up with a very good answer. The most general definition one can give for an object to be ...
- 4,500
1vote
0answers
34views
Is it possible to demand a thermal initial state in the closed time contour Keldysh formalism?
The Keldysh path integral derived from a Lindblad-equation on a closed time contour in coherent state representation reads $$ Z = \int\mathcal{D}[\Psi_+,\Psi_-]e^{iS[\Psi_+,\Psi_-]}\langle\Psi_+(0)|\...
7votes
2answers
313views
Tree-level of two-point function
I am currently learning AQFT (advanced QFT) with the lecture notes of Osborn (I've had a course on QFT but this was not with the path integral formalism) and at some point he says the following $$\...
- 105
2votes
0answers
78views
Faddeev-Popov method, insertion of identity
Question 1: Understanding the Faddeev-Popov determinant in gauge theory In quantum field theory, we encounter difficulties when quantizing gauge theories because of redundancies in the path integral. ...
1vote
1answer
109views
How to relate $\langle 0| \phi(x) |0\rangle$ with Feynman diagrams to a $\phi^3$ theory without counterterms?
I am learning QFT on my own via Mark Srednicki's book, and I have a bit of trouble following the author in chapter 9, where the path integral for an interacting theory is introduced, as well as ...
- 175
0votes
1answer
109views
Gaussian integral in QFT
I would like to perform this (basic) integral in QFT: where $a$ is a constant $$ \int D\phi D\phi^*e^{-\int d^4x \phi^* M\phi+a(\phi+\phi^*)} $$ The general formula is $$ \int D \varphi^{\dagger} D \...
- 445
1vote
2answers
120views
Convergence of Euclidean path integral
Can you explain why they say, that the Euclidean path integral converges? Naively, it diverges because in the Lagrangian, when calculating the kinetic term, we take the difference between neighbouring ...
- 375
3votes
0answers
76views
In QFT, what happens when we only integrate over paths inside light cone? [closed]
In the path integral picture of QFT, we have to integrate over all paths connecting two states. What happens when we only integrate over paths that don't violate causality? Since the paths that are ...
1vote
1answer
144views
Path integral in QFT
In QM we use $$\langle x_{f}|e^{-{\frac {i}{\hbar }}H(t_{f}-t_{i})}|x_{i}\rangle={\lim _{N\to \infty }\int\left(\,{\frac {m}{2\pi i\hbar \epsilon }}\,\right)^{N/2}\ e^{\frac{iS}{\hbar}}\prod _{j=1}^{N-...
- 1,318
1vote
0answers
47views
Functional equation (6.156) in the book "QFT" by Lewis Ryder
I have 2 questions regarding Eq. $6.155$ to Eq. $6.156$ in Ryder's QFT book. In Eq. $6.155$, why do we multiply the functional $I[J]$ from the left of $\phi_{in}(x)$ and then from the right of $\phi_{...
- 153
1vote
1answer
108views
Is the Trotter formula justified in a theory that requires renormalization?
Usually, when QFT textbooks attempt to prove the equivalence of the path integral formulation with more familiar matrix mechanics, we make use of the Trotter formula. In Euclidean time, with $\hat{H}=\...
- 4,164
3votes
2answers
165views
Sum over histories inside a Black Hole
I am considering how a particle (described by a quantum field) behaves inside a black hole, assumed large and old (for smoothness and depth). This is something like QFT in a relativistic setting. The ...
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