Linked Questions

14
votes
1answer
884 views

Divergent integrals in QFT

I am starting to learn about QFT and something that I noticed is that integrals who would diverge otherwise are assigned a value if we do it by contour integration using the residues theorem and the ...
3
votes
1answer
1k views

How to choose the Correct Green's Function?

In order to solve the Green’s function of the Helmholtz operator $$(\nabla^2+k^2)G(\vec r-\vec r’)=\delta^{(3)} (\vec r-\vec r’)$$ one can obtain four different Green’s functions corresponding to four ...
3
votes
2answers
874 views

Feynman's $i \epsilon$ prescription in loop expansion

I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity? And third, Dyson ...
3
votes
1answer
666 views

Fluctuation-dissipation theorem in QFT

If I understand correctly, the fluctuation-dissipation theorem (fdt) in QFT technically arises because of $\pm i\epsilon$ - infinitesimally small summand in the denominator of spectral representation ...
3
votes
1answer
665 views

The $i\epsilon$ in non-relativistic scattering theory

When doing quantum mechanical scattering theory, we obtain the Lippman-Schwinger equation $$|\psi\rangle=|\psi_0\rangle+(E-H_0)^{-1}V|\psi\rangle$$ Here $\psi_0$ is the unperturbed wavefunction, $\...
1
vote
2answers
192 views

Does the property of being “virtual” for a particle depend on the observer?

I've read at several places that a static magnetic (and electric for that matter) field can be thought of as made by virtual photons, at least that's what I understood. Now, in Special Relativity we ...
1
vote
2answers
458 views

Sum of Green's functions in condensed matter

I am working on the Ginzburg-Landau model for Charge density waves, and I am carrying out the sum of Green's functions to calculate the terms in the GL model. Is the sum's order over $ \vec{k} $ (or ...
5
votes
1answer
259 views

Different possible solutions for the wave equation?

The Wave equation is: $$\nabla^2\psi(\mathbf{x},t)-\frac{1}{c}\frac{\partial^2 \psi(\mathbf{x},t)}{\partial t^2}=f(\mathbf{x},t)$$ The Green function is then $$\nabla^2G(\mathbf{x},t)-\frac{1}{c}\...
0
votes
1answer
300 views

$i\epsilon$ in CFT correlation functions

M. Luescher in his talk on p.6 writes that the 2-point correlation function of a Hermitian local field $O_k$ of scaling dimension $d=3-k$ looks like $$ \langle 0| O_k(x) O_k(y) |0\rangle = A_k (x-y-i ...
2
votes
1answer
379 views

Pole of a free-particle propagator

The free-particle propagator is given by $$\Delta_F(x-y) = \frac{1}{(2\pi)^4} \int \frac{e^{-ik\cdot(x-y)}}{k^2-m^2+i\epsilon} \, d^4k.$$ In the book Quantum Field Theory, Ryder says that $\Delta_F(x-...
5
votes
1answer
481 views

How uniquely determined is the impedance of an infinite-chain circuit?

A recent question asked how to find the impedance of an infinite chain of series-plus-parallel circuits. The standard trick is to split the chain after the first link, and treat the tail of the ...
2
votes
3answers
171 views

Use of negative frequency for the sake of simplifying mathematics?

How can we use the idea of negative frequency for the sake of simplifying mathematics if negative frequency does not exist (to my knowledge) in nature ? For example, when plotting the spectra of a ...
0
votes
1answer
127 views

Path integral calculations $e^{i\omega 0^+}$

When computing correlation functions using the path integral formulation, I often need to compute integrals such as $$ \int_{-\infty}^\infty \frac{d\omega}{2\pi} \frac{1}{i\omega -\epsilon} $$ ...
3
votes
0answers
171 views

Non-equivalence between $\omega \to \omega \pm i\varepsilon$ and Cauchy principle value

I am looking to gain a more rigorous and deeper understanding as to how an $i\varepsilon$ prescription actually changes the end result of a divergent integral, specifically in regards to Green's ...
1
vote
0answers
85 views

What classes should i choose in order to study theoretical physics? [closed]

I am an undergraduate physics student who wants to be a theoretical physicist. The math department in my uni offers the following sequences of classes: ~Analysis 1 -> Analysis 2 -> Topology ~...