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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.

2 votes
Accepted

Is the sign of an amplitude in QFT meaningful?

The phase of a quantum-mechanical probability amplitude is completely arbitrary – this is in fact one of the fundamental postulates of quantum mechanics. A quantum-field-theoretic scattering amplitude …
AccidentalFourierTransform's user avatar
4 votes

Can Feynman diagrams be used to represent any perturbation theory?

If we stretch the definition of a Feynman diagram, then yes: the technique can be applied to any problem where you use perturbation theory. But if by Feynman diagram you mean the exact same philosophy …
AccidentalFourierTransform's user avatar
2 votes
Accepted

Photon propagator counterterm in QED

An arbitrary interaction of the form $$ \mathcal L_\mathrm{int}=\frac{g}{n_1!\ n_2!\ \cdots \ n_j!}\phi_1^{n_1}\phi_2^{n_2}\cdots\phi_j^{n_j} $$ where all the $\phi_i$ are different, has an associated …
AccidentalFourierTransform's user avatar
3 votes
Accepted

Terminology for "one-loop" in position space?

Short answer. Your second option is correct. Longer answer. A Feynman diagram is nothing but a graph, in the sense of graph theory. It is mapped to $\mathbb C$ (or, more precisely, the ring of form …
AccidentalFourierTransform's user avatar
8 votes
Accepted

Terminology of 1PI diagram

It is a convention that simplifies some formulas. You can always choose to include the propagators on the external lines, but their effect is rather trivial so they don't add relevant information to …
AccidentalFourierTransform's user avatar
26 votes
Accepted

Feynman diagram and uncertainty

There are no axes in Feynman diagrams. The only important part of a diagram is what is connected to what, and not the relative orientation. You can move around the pieces of a diagram and, as long as …
AccidentalFourierTransform's user avatar
4 votes
Accepted

Guessing of the vertex factor of derivative interactions

Your derivation is indeed sometimes used as a shortcut to argue that a derivative interaction corresponds to a factor of momentum for each derivative. Unfortunately, it is far from convincing for seve …
AccidentalFourierTransform's user avatar
0 votes
Accepted

Question about superficial and real degree of divergence

Hint: consider the box diagram (From Wikipedia) For more details about this diagram, see chapter 10.1 in Peskin&Schroeder (e.g., fig. 10.2, and the discussion around eq. 10.6), and problem 10.1 (y …
AccidentalFourierTransform's user avatar
6 votes
Accepted

(No) Field Renormalization in $\phi^4$ theory at one-loop

There is no intuition, really. In this particular theory, the first order contribution to the wave strength renormalization just happens to vanish. Why does it vanish? Well, this constant comes from t …
AccidentalFourierTransform's user avatar
39 votes
Accepted

Systematic way to draw all inequivalent Feynman diagrams

OP has discovered on their own a primitive application of the Schwinger-Dyson equations. Congratulations! A very gentle introduction to the Schwinger-Dyson equations. ... or how to calculate correla …
AccidentalFourierTransform's user avatar
19 votes

Non-Perturbative Feynman diagrams?

If the theory is Borel summable, you can recover non-perturbative information from the perturbative series. This can be shown explicitly for example by calculating the exact effective action in the pr …
AccidentalFourierTransform's user avatar
2 votes
0 answers
146 views

Feynman rules with other propagators$.$

An arbitrary correlation function $$ G_F(x_1,\dots,x_n)=\langle 0|\mathrm T\ \phi(x_1)\cdots\phi(x_n)|0\rangle\tag1 $$ can be calculated in perturbation theory by adding all Feynman diagrams, with the …
AccidentalFourierTransform's user avatar
1 vote
0 answers
189 views

Recurrence relations for tree-level Feynman diagrams

Consider a certain quantum mechanical system with action $S[\phi]$, and let $$ G(1,\dots,n)\equiv\langle\phi_1\cdots\phi_n\rangle $$ be the $n$-point function. It is well-known that these functions sa …
AccidentalFourierTransform's user avatar
4 votes
1 answer
598 views

Loop counting -- what if the graph is not planar?

It is typically claimed that $\hbar$ counts the number of loops in a connected diagram. E.g., Weinberg's QFT, Vol.II, equation 16.1.10. This rests on the fact that for a diagram with $I$ internal line …
AccidentalFourierTransform's user avatar
2 votes
Accepted

Overall plus or minus sign in scattering amplitudes when calculating Feynman diagrams

As long as you are consistent, the overall phase of $\mathscr M$ is irrelevant. Not even the $i$ is really important.
AccidentalFourierTransform's user avatar

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