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6
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1answer
134 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 + ...
4
votes
1answer
210 views

Relation between symmetry factors

In $\phi^3$ theory, the generating functional for interacting field theory is given by: $$ Z_1(J) = \sum_{V=0}^{\infty} \frac{1}{V!} \Big[ \frac{iZ_g g}{6} \int \Big( \frac{1}{i}\frac{\delta}{\delta ...
3
votes
1answer
178 views

Feynman Diagram for Bragg Equation

Did Feynman ever derive the Bragg equation as a particle representation using Feynman diagrams? And where is it available? I spoke to Freeman Dyson and he couldn't recall.
7
votes
0answers
317 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 ...
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} ...
6
votes
0answers
245 views

An use of the Schwinger-Dyson equation

I was confused as to how the equation 10 on page 7 or equation 21 on page 8 of this paper http://arxiv.org/abs/1211.1866 was derived. Can someone explain from where does this come and what do the ...
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 ...
5
votes
0answers
137 views

Understanding the intermediate field method for the $\phi^4$ interaction

In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to ...
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 ...
5
votes
0answers
218 views

How fat is Feynman’s photon?

According to my calculations, it is a lot skinnier than Airy’s photon, but still a whole lot fatter than a straight line. So, how does a photon get from point A to Point B? The ray optics ...
4
votes
0answers
41 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
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 ...
4
votes
0answers
128 views

gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
4
votes
0answers
57 views

Helicity dependence in loop diagrams

I am trying to evaluate a diagram that looks like The middle of the diagram is a fermion loop. I know that the coupling between the $Z^0$ and fermions depends on the fermions' helicities, so it ...
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
31 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: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$ ...
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 ...
3
votes
0answers
57 views

Feynman Toy Model Constraints on Number of Each Kind of External Lines

(From my homework) In our toy model we have three kinds of spinless particles: $A$, $B$, and $C$. The primitive vertex of decay/interaction is shown below: My actual problem statement says: ...
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 ...
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 ...
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 ...
3
votes
0answers
44 views

Scattering theory on Schrodinger and Feynman languages

Recently I heard that both of "languages" of scattering theory (formal solution by method of classical scattering theory and its reworking by Feynman with his rules) predict virtual particles. But for ...
2
votes
0answers
39 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} ...
2
votes
0answers
64 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 ...
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 ...
2
votes
0answers
41 views

Approximation of skeleton diagrams

I'm studying the diagrammatics for a Bose system (in the superfluid phase) developed by Gavoret and Nozieres (Annals of Physics 28 349 (1964)). In this paper, they show how to solve the problem using ...
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?
2
votes
0answers
77 views

Chirality when moving around legs in Feynman diagrams

Assuming one has the following term in a Lagrangian: $$ g (\overline{A_R} B_L)(\overline{C_R}D_L) $$ where A,B,C,D correspond to spin 1/2 Dirac particles and the subscripts $R$ and $L$ denote left- ...
1
vote
0answers
25 views

Sign of Feynman rules with derivative couplings

Feynman rules for derivative couplings always make me confused. For example, the derivative in $gV^\mu\phi^+\partial_\mu\phi^-$ will give you $\pm ip_{-\mu}$, where $\pm$ depends on whether the ...
1
vote
0answers
22 views

Physical interpretation of scalar tadpole loops

In Feynman diagrams, fermionic loops are drawn like this: While scalar loops are drawn as tadpoles: I assume the difference comes from the scalar not having an anti-particle. But how should one ...
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 ...
1
vote
0answers
85 views

Two forms of Feynman Diagrams?

I am confused. I know Feynman Diagrams looks like the ones here. But then I saw these, look in page 17[1247] of this paper. Any idea?
1
vote
0answers
177 views

Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...
1
vote
0answers
77 views

Exact summation of a sub-class of diagram: do we know the exact solved problem?

In quantum field theories (to be relativistic, (non-)relativistic statistical or whatever), we have the powerful diagrammatic approach at our disposal. Most of the time we can not sum up all the ...
1
vote
0answers
87 views

Feynman Diagram for Interaction of Deuteron with Oxygen-16

I have to draw a Feynman diagram for the interaction of a deuteron with Oxygen-16. The interaction is as follows: $ d + {}^{16}O \rightarrow p + {}^{17}O . $ I am generally ok with Feynman ...
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 ...
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 ...