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Results tagged with feynman-diagrams
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user 36793
A diagrammatic technique introduced by Richard Feynman to describe the quantum behaviour of subatomic particles and their interactions. Do not use for general questions on diagrams that are not of the Feynman kind.
11
votes
1
answer
2k
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How does chirality of a massive fermion change with time?
For a massive fermions, like the electron, chirality is not conserved in time. It is not a good quantum number although it is Lorentz invariant. The Dirac Hamiltonian (in particular, the mass term in …
- 27.2k
7
votes
3
answers
741
views
Criterion for a Feynman loop diagram to give a finite value
The contribution of loop diagrams in QFT are often divergent and sometimes convergent as well. For example, the self-energy corrections in QED are divergent. On the other hand, the Zee model of radiat …
- 27.2k
6
votes
3
answers
1k
views
How does a perturbation theory make sense in quantum field theory?
The idea of a perturbation series in powers of a coupling $\alpha\ll1$ (for example, the fine structure constant in QED) make sense if the contribution of $(n+1)^{th}$ term in the series is smaller th …
- 27.2k
5
votes
2
answers
1k
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Possible divergence structures of a renormalizable and non-renormalizable theory
If a theory has a coupling with negative mass dimension, it will require an infinite number of counterterms. This is because the theory will have infinitely many divergence structures.
To be concrete …
- 27.2k
4
votes
1
answer
479
views
Physical interpretations of the generating functions $Z[J]$ and $W[J]$ (or $E[J]$)
In quantum field theory, the generator of all Green's functions $Z[J]$ and that of the connected Green's functions $E[J]$ are related as $$Z[J]=\exp[-iE[J]]=\int D\phi\exp[i\int d^4x(\mathcal{L}(\phi) …
- 27.2k
3
votes
0
answers
1k
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Symmetry factor for 1PI Feynman diagrams in $\phi^4$ theory
I am trying to understand the various factors that the Feynman amplitude will carry corresponding to the Feynman diagrams of Fig. 1 of this reference. I understand that the $n^{th}$ diagram containing …
- 27.2k
3
votes
0
answers
275
views
External momenta vs loop momenta in Feynman diagrams
In Peskin and Schroeder's book on QFT, the second paragraph of chapter 12 says,
In a renormalizable theory, the loop integrals over virtual-particle momenta are always dominated by values comparab …
- 27.2k
3
votes
Accepted
Divergence of Feynman diagram
Consider a generic Feynman diagram with,
$L$ loops, $N_f$ number of internal fermion lines (or fermionic propagators) and $N_b$ number of internal boson lines (or bosonic propagators),
different ki …
- 27.2k
3
votes
1
answer
1k
views
Total divergence term and corresponding Feynman Diagram
A total divergence term added to the Lagrangian doesn’t affect the action because the integral of a total divergence vanishes. But if one attempts to derive the Feynman rules from the Lagrangian with …
- 27.2k
3
votes
2
answers
2k
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How to tell whether a Feynman diagram is $t$-channel or $s$-channel by looking?
By looking at a diagram, how does one tell whether it represents a $s$-channel process or a $t$-channel process i.e., without finding the amplitude? I'm familiar with Mandelstam variables but I've tro …
- 27.2k
1
vote
1
answer
106
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Understanding massive internal boson line and its virtual nature
Consider the scattering $$e^-(p_1)+e^+(p_2)\rightarrow e^-(p_1^\prime)+e^+(p_2^\prime)$$ at the tree-level via a internal photon line of four-momentum $q$. Using energy momentum conservation at the ve …
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1
vote
How to tell whether a Feynman diagram is $t$-channel or $s$-channel by looking?
For a two-body scattering process denoted by $$a_1(p_1)+a_2(p_2)\to a_3(p_3)+a_4(p_4)$$ the tree-level Feynman diagrams can be classified into three categories. A tree-level scattering diagram is call …
- 27.2k
1
vote
2
answers
425
views
Can one forget about the contribution of 1PR diagrams in computing a scattering amplitude?
From the LSZ reduction formula, it is clear that only the connected Feynman diagrams that contribute to a scattering amplitude. However, connected diagrams are of two types: 1PR and 1PI. 1PR diagrams …
- 27.2k
0
votes
1
answer
274
views
Little confusion in drawing Feynmam diagram
If the arrows of both the outgoing solid lines of the Feynman diagram corresponding to the Bhabha scattering of $e^+$ and $e^-$ are just reversed, will it not describe the same thing? Doesn't both imp …
- 27.2k
0
votes
Understanding massive internal boson line and its virtual nature
I've worked out the answer to my own question and here I'll attempt to answer it.
Let us assume the massive internal boson line is on-shell i.e., $q^2=M_Z^2$. Now, $$p_1-p_1^\prime=q\Rightarrow p_1^ …
- 27.2k