2
votes
0answers
29 views

S-Matrix Generating Functional (Problem 4.1 in Weinberg)

I'm currently working through Weinberg's QFT book, but I'm somewhat stuck at problem 4.1, which states: Define generating functionals for the S-matrix and its connected part: \begin{equation} ...
5
votes
1answer
119 views
+50

Coleman-Weinberg potential: resum at 2 loops?

Say we want to compute the Coleman-Weinberg potential at 2 loops. The general strategy as we know is to expand the field $\phi$ around some background classical field $\phi \rightarrow \phi_b + ...
3
votes
0answers
67 views

Topologically distinct Feynman diagrams

Are these two diagrams topologically distinct? I consider $\phi^4$ theory and use MS-scheme. A vertex corresponding to counterterm $-\imath \frac{m^2 \lambda}{32 \pi^2 \epsilon}$ is denoted by ...
3
votes
0answers
30 views

What is the phase space for outgoing photons?

For a scattering process for which $n$ fermions are scattered, (by some conventions) the cross section acquires a phase space factor of: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$ ...
1
vote
1answer
53 views

Symmetry factor of $n$-point one-loop diagram [duplicate]

If we have a one-loop diagram in $\phi ^ 3$ scalar field theory with $n$ external lines, then what is its symmetry factor? I have drawn the diagram I am looking for, but instead of $6$ external ...
3
votes
1answer
77 views

Symmetry factor of Feynman diagram

What is the symmetry factor for the following Feynman diagram if we assume that the external points are held fixed? Please ignore the arrows in the diagram. I am referring to the second diagram on ...
6
votes
3answers
245 views

Can photons have negative energy?

Apparently there are 2 electron self-energy graphs possible. The first, the more "familiar", where the incoming electron at time $t_1$ splits up in a photon and an virtual electron. At $t_2>t_1$ ...
6
votes
0answers
83 views

Deriving Feynman rules from Renormalized Lagrangian

In the context of Renormalized Pertubation Theory Peskin Schröder says: The Lagrangian $$ \mathcal{L}=\frac{1}{2} (\partial_\mu\phi_r)^2-\frac{1}{2}m^2\phi_r^2-\frac{\lambda}{4!}\phi_r^4 + \frac{1}{2} ...
4
votes
0answers
41 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
1
vote
1answer
50 views

What is the leading order Feynman diagram for nucleon-anti-nucleon annihilation into two mesons ($\psi^{\dagger} \psi \to \phi\phi$)?

I am working with a standard basic scalar Yukawa theory. I.e. the only interaction term is $-g\psi^\dagger\psi\phi$, where the $\phi$ field quanta are the mesons, the $\psi$ field quanta are the ...
1
vote
0answers
29 views

Estimation of polarization perturbative term

I'm studying a diagrammatic approach to degenerate electron gas. Now I need to prove that the energy contribution, with an arbitrary potential, of polarization at first perturbative order given by the ...
17
votes
3answers
563 views

The path integral and Feynman diagrams

This question is somewhat of a historical one, but it also contains some physics. I am curious to find how exactly the concept of Feynman diagrams arose (I assume from Feynman's path integral)? The ...
0
votes
0answers
43 views

Feynman Rules in Momentum space

What's the difference between Feynman rules in momentum space for $\phi^3$ theory and for $\phi^4$ theory? I know it's only a slight difference and perhaps found in the vertex factor? But for some ...
1
vote
1answer
102 views

Feynman Diagram in $\phi^3$ theory

I'm slightly befuddled by is what it means when I'm asked to Draw the Feynman diagram in momentum space for the two point function of $\frac{\lambda}{3!}\phi^3$ theory for order $O(\lambda^2).$ ...
3
votes
0answers
52 views

Symmetry factor of tree diagram

In Mark Srednicki's Quantum field theory(page 89) it says This is a general result for tree diagrams (those with no closed loops): once the sources have been stripped off and the endpoints ...
2
votes
0answers
60 views

Feynman rules of a theory in non-standard form

I am currently studying lecture notes by Akhmedov on interacting scalar field theory in de Sitter space. In these notes, he considers a scalar field theory of the form ...
5
votes
1answer
170 views

A question about Feynman diagram and symmetry factor

Consider a $\varphi^3$ theory: $$ Z_1(J) \propto \exp\left[\frac{i}{6} Z_g g\int \mathrm{d}^4 x \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right] Z_0(J), $$ where $$ Z_0(J) = ...
3
votes
1answer
69 views

Is there a way to compute (trivalent) Feynman integrals inductively from smaller diagrams?

Suppose that I would like to compute the Feynman integral associated to the trivalent graph One can argue that this diagram comes from two copies of the smaller diagram glued together at the ...
2
votes
1answer
53 views

All angle dependence in $\mathrm{d}LIPS_2$?

Recall that $\mathrm{d}LIPS_2$ (one particle decaying into two particles of the same mass) is given by $$\mathrm{d}LIPS_2 = \frac{\vert{\bf k_1'}\vert}{16\pi^2\sqrt{s}}\mathrm{d}\Omega_{cm}.$$ In a ...
5
votes
0answers
100 views

Functional integral aproach for Feynman rules

I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or ...
1
vote
1answer
114 views

How to prove useful property of logarithm of generating functional in QFT?

How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.
3
votes
0answers
94 views

Why do we use functional integration in QFT?

Recently I learned functional integral's formalism in QFT. I have realized that I don't understand why exactly do we introduce it. We have the expression for $S$-matrix, then we may rewrite it in ...
4
votes
1answer
173 views

QED Vertex Factor/Rule

On page 303 in Peskin&Schroeder they give the vertex factor as $$V = -ie\gamma^\mu \int d^4x$$ while on page 304 they write $$V_\times = -ie\gamma^\mu\int d^4x A_\mu(x).$$ Why are the ...
3
votes
2answers
122 views

Field Strength Renorm in Peskin&Schroeder

On page 237 in PS we have (the unnumbered equation after eq. 7.58) $$\mathcal{P} \sim \frac{iZ}{p^2-m^2-iZ\,\mathrm{Im}M^2(p^2)}$$ but after deriving it myself I obtained $$\mathcal{P} \sim ...
0
votes
1answer
101 views

Little confusion in drawing Feynmam diagram

If the arrows of both the outgoing solid lines of the Feynman diagram corresponding to the bhabha scattering of $e^+$ and $e^-$, are just reversed, will it not describe same thing? Doesn't both imply ...
4
votes
0answers
92 views

Can $\langle\Omega|f|\Omega \rangle$ always be reduced to $\langle0|f|0\rangle$?

I've not come across any expression involving $\langle\Omega|f|\Omega\rangle$ in Srednicki's QFT book (please correct me if these exist there). On the other hand, they are abound in Chapter 7 of ...
3
votes
0answers
68 views

Vertex for quartic interaction of complex scalar multiplet

Since I'm new to QFT and I tend to do a lot of errors during calculations, I would like you to tell me if I got the four-point vertex of the quartic interaction with a multiplet of complex scalar ...
7
votes
2answers
155 views

Tadpole symmetry factor

Can someone help me with symmetry factor of one-loop tadpole diagram (one loop correction to one point Green function in phi-3 theory)?
6
votes
2answers
205 views

Feynman Diagrams in 2 component notation

When using two component notation people often prefer to refrain from using arrows in Feynman diagrams to denote charge flow as is done in four-component notation. Instead, if understand correctly, ...
2
votes
1answer
111 views

What is the difference between QFT and elementary particle physics?

I'm a little unclear as to how QFT differs from Elementary particle physics. They both use pictorials of Feynman graphs, is it that Elementary particle physics assumes the point particle perspective, ...
9
votes
1answer
447 views

Software for calculating Feynman Diagrams

Is there a software (open source preferred) where I would input something like "Ingoing: a fermion $(p1, s1)$ and a photon $(p2, s2)$. Output: A fermion $(k1, r1)$ and a photon $(k2, r2)$" and I would ...
3
votes
1answer
92 views

Equation 7.22 in Peskin & Schroeder: writing the Fourier transform of a two-point function as a series of 1PI diagrams

In Peskin and Schroeder's QFT book, on page 219, there is the following equation: The heading to the equation is: "The Fourier transform of the two-point function can now be written as". Could ...
3
votes
1answer
279 views

Feynman rules for real scalar field interacting with electromagnetic field

I was wondering if anyone could help guide me in finding the Feynman rules for a real pseudoscalar field ($\phi$) interacting with the electromagnetic field $(F^{\mu\nu})$. The (effective) ...
3
votes
2answers
200 views

$2\pi$ and Feynman Rules

I notice a $2\pi$ term in the $\delta$-function when trying to construct an amplitude using the Feynman Rules. The $2\pi$ also appears as an integration measure to enforce normalisation in the phase ...
4
votes
1answer
308 views

How can we derive the Feynman rule for the ordinary QED 3-vertex?

I have checked some Quantum Field Theory texts that include basic QED and they all include the Feynman rule that each vertex bring with it a factor of $$\pm i e \gamma^\mu$$ but I have yet to find a ...
2
votes
1answer
239 views

Feynman propagators for scalar fields

If there are few massless scalar field, are the propagators of those different massless scalar fields indistinguishable?
7
votes
0answers
316 views

Where does the divergence in the $g\phi^3$ $d=4$ 3 point one loop diagram (three external legs) come from?

$g\phi^3$ , $d=4$ , 3 point One loop diagram (three external legs) Divergence I am trying to find where the divergence factor/pole is on the following diagram in 4 dimensions so that I can use ...
3
votes
1answer
246 views

Connected and strongly connected Feynman diagrams

Recently I read, that only connected Feynman diagrams give contribution of nonzero values into the scattering amplitude. Why it is so and what is the physical sense of connected diagrams (due to ...
3
votes
0answers
121 views

Feynman rule for deriative interaction: an example

Consider a theory for a finite number of real scalar fields $\phi _i$ with interaction terms of the form $$ -\lambda _{ijk}\phi _i\partial _\mu \phi _j\partial ^\mu \phi _k, $$ with the sum over ...
1
vote
1answer
59 views

Allowed interactions for the neutral weak vector boson

Just wanted to double check a couple of things for my own sanity! I am looking at scattering amplitudes for 2 partons going to two partons with the emission of a Z boson (eventually decaying to e+ ...
0
votes
1answer
305 views

If time travel to the past is not possible why is this situation considered in Feynman diagrams?

I recently read R.P Feynman's QED:A Strange Theory of Light and Matter. It is believed that time travel to the past is not possible. Then why is particles going backward in time considered in the book ...
2
votes
1answer
168 views

Feynman diagrams for interacting theory of scalar field

Is it correct that the number of lines originating from vertices on Feynman diagrams is equal to the order of phi in interaction lagrangian for scalar field?
2
votes
1answer
152 views

Why does the counterterm's propagator have inverse units of the propagator? $\phi^4$-theory

According to Peskin & Schroeder (page 325), the Feynman rule for the counterterm ------(x)----- for $$ \frac12 ...
2
votes
0answers
89 views

Møller scattering: twisted?

I am studying the Møller scattering, but I don't know how to get the twisted diagram from the S-matrix. Has anybody a good explanation?
5
votes
1answer
342 views

Scattering amplitude and LSZ formula

I'm arriving at a contradiction. To calculate the scattering amplitude, one usually follows the prescription given by the Feynman rules that you only consider fully connected diagrams with the ...
5
votes
0answers
414 views

If Renormalization Scale is Arbitrary, Why Do We Care about Running Couplings?

For the bounty please verify the following reasoning [copied from comment below] Ah right, so the idea is that overall observable quantities must be independent of the renormalization scale. But at ...
2
votes
1answer
153 views

Scalar two loop diagram in $\varphi^4$ theory

Could someone explain how, or at least show me a link that explicitly shows the calculation of a two-loop corrections to scalar’s two-point function in $\varphi^4$ theory in the massless limit.
3
votes
1answer
184 views

Minus Sign in Feynman Diagram

I've been reading these notes and I can't figure out the why on P.120, it is said that The fermionic statistics mean that the first diagram has an extra minus sign relative to the ψψ scattering ...
0
votes
0answers
56 views

Reduced graphs and pinch-singular surfaces

I am reading a book on perturbative QCD by John Collins. In Chapter 5, the terms reduced graph and pinch-singular surface are used for the analysis of mass singularities. However, their meanings are ...
3
votes
1answer
425 views

Evaluation of QED amplitude with 1 external photon

I'm trying to compute the exact QED amplitude with one external photon. Suppose that the photon has 4-momentum $q$ and polarization $\varepsilon^\mu$. Peskin and Schroeder (p318) claim that ignoring ...