Questions tagged [feynman-diagrams]

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.

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32
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4answers
11k views

Do virtual particles actually physically exist?

I have heard virtual particles pop in and out of existence all the time, most notable being the pairs that pop out beside black holes and while one gets pulled away. But wouldn't this actually violate ...
18
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4answers
16k views

What would the collision of two photons look like?

Could someone explain to me what the collision of two photons would look like? Will they behave like, Electromagnetic waves: they will interfere with each other and keep their wave nature Particles: ...
13
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3answers
874 views

Use my example to explain why loop diagram will not occur in classical equation of motion?

We always say that tree levels are classical but loop diagrams are quantum. Let's talk about a concrete example: $$\mathcal{L}=\partial_a \phi\partial^a \phi-\frac{g}{4}\phi^4+\phi J$$ where $J$ is ...
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4answers
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Proof of Connected Diagrams

If $Z[J]$ is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $$W[J]\equiv\frac{\hbar}{i}\log\left(Z[J]\right)$$ "generates" only ...
6
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2answers
2k views

Intuition behind Linked Cluster Theorem: connected vs. non-connected diagrams

Within statistical physics and quantum field theory, the linked cluster theorem is widely used to simplify things in the calculation of the partition function among other things. My question has the ...
4
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1answer
1k views

Why don't virtual particles violate conservation of mass/energy?

If virtual particles sometimes add more mass/energy to a system then was inputed or comes out in the output, how do they not violate conservation of mass/energy.
12
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2answers
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Why do the counterterms in renormalized $\phi^4$-theory with power two in fields give vertices and not propagators?

I am reading Peskin and Schroeder, chapter ten, and my Lagrangian is $$ \mathcal{L}=\frac{1}{2}(\partial_\mu\phi_r)^2-\frac{1}{2}m^2\phi_r^2-\frac{\lambda}{4!}z^2\phi^4+\frac{1}{2}\delta_Z(\partial_\...
3
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2answers
1k 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.
4
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1answer
1k views

How do I derive the Feynman rules for graviton-photon coupling?

I am trying to study the coupling of the graviton field $h_{\mu\nu}$ to the electromagnetic field $A_\mu$ with respect to the following action: $$ S_M = \int d^4x \ \sqrt{-g} \ (-\frac 1{4} g^{\mu\nu}...
1
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1answer
343 views

Virtual Photon in Electron Scattering Feynman diagram [duplicate]

If we know that the virtual photon emitted in an electron scattering Feynman diagram violates the energy and momentum conservation laws (though temporarily), why do we accept it as a feasible diagram ...
16
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1answer
1k views

Systematic way to draw all inequivalent Feynman diagrams

I am wondering whether there is some systematical approach to find Feynman diagrams for S-matrix (or to be more precise for $S-1$ since I am interested in scattering amplitude). For example in $\phi^3$...
10
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3answers
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Electron Positron annihilation Feynman Diagram

I am having some trouble understanding this fenyman diagram, it seems to indicate that the electron produces the positron, as the arrow of the positron is pointing from the electron. Additionally the ...
6
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2answers
1k views

Feynman diagram for attractive forces

I’m looking at Feynman diagrams for attractive forces and I'm thoroughly confused. Below are three diagrams from HyperPhysics: These all illustrate instances where the forces are attractive. However, ...
18
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3answers
4k views

Problem understanding the symmetry factor in a feynman diagram

I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are in $\phi^4$ ...
9
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2answers
480 views

Why does normal ordering violate the Ward identity?

It is well known that normal ordering the Lagrangian eliminates all Feynman diagrams with tadpoles$^{[1]}$. In the case of the photon self-energy in scalar QED, one of the diagrams is, in fact, a ...
2
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2answers
1k views

How do you prove that $L=I-V+1$ in $\lambda\phi^4$ theory?

It is known that the number of loops in $\lambda\phi^4$ theory is given by the formula $$L=I-V+1$$ where $L$ is the number of loops, $I$ the number of internal lines and $V$ the number of vertices. ...
8
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3answers
1k views

What makes a Feynman diagram real or virtual?

Simple question: as the title says, what makes a real Feynman diagram real, and what makes a virtual diagram virtual? Or in other words, how do I tell whether any given diagram is real or virtual? I'...
3
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1answer
2k views

Formula for Symmetry Factor

In $\phi^3$ theory, are there any formula for determining the Symmetry factor as that is found for the $\phi^4$ theory in any standard book of Quantum Field Theory?
2
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1answer
498 views

Virtual Photon transmission speed of a Static Electric Field?

In the case of a non-accelerating point charge "A" of stable velocity, its static field is treated as though it is instantaneously present at a distance, i.e. a second point charge "B" will react to ...
2
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1answer
260 views

Proof of geometric series two-point function

In deriving the expression for the exact propagator $$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$ for $\phi^4$ theory all books that i know use the following argument: $$G_c^{(2)}(x_1,x_2)=G_0^{(2)}...
22
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3answers
7k views

Gentle introduction to twistors

When reading about the twistor uprising or trying to follow a corresponding Nima talk, it always annoys me that I have no clue about how twistor space, the twistor formalism, or twistor theory works. ...
13
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3answers
876 views

Does radio use virtual photons?

In radio communication each accelerated electron in the transmitter antenna interacts with an electron in the receiver antenna by exchanging a photon. Is that photon always a virtual photon as ...
7
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1answer
600 views

Truncated $N$-Point Functions

In Quantum Field Theory, truncated N-Point functions (or truncated Green's functions) are the N-Point functions of diagrams with their external legs chopped off. I was told that the truncated N-Point ...
3
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1answer
778 views

Do we really need virtual particles to exist?

I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, ...
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2answers
1k views

How do derivative couplings affect canonical quantization?

Consider a Lagrangian for a scalar field $\phi$ with an interaction term $$\mathcal{L}_{int} = (\partial^2 \phi)^2 \phi.$$ Here I'm suppressing all indices for brevity. Now, this is just a three-...
3
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2answers
3k views

$\mathrm{\rho^0}$ meson decay via the weak interaction?

Of course, the $\mathrm{\rho^0}$ meson can decay in $\mathrm{\pi^{+}\ \pi^{-}}$ through the strong interaction. Using Feynman diagrams, I cannot understand why the same decay couldn't happen through ...
22
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1answer
7k views

Interpretation of derivative interaction term in QFT

I am trying to understand what a term like $$ \mathcal{L}_{int} = (\partial^{\mu}A )^2 B^2 $$ with $A$ and $B$ being scalar fields for instance means. I understand how to draw an interaction term in ...
19
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5answers
2k views

Can Feynman diagrams be used to represent any perturbation theory?

In Quantum Field Theory and Particle Physics we use Feynman diagrams. But e.g. in Schwartz's textbook and here it is shown that it applies to more general cases like general perturbation theory for ...
16
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2answers
985 views

Non-Perturbative Feynman diagrams?

The Wikipedia page for Feynman Diagrams claims that Thinking of Feynman diagrams as a perturbation series, nonperturbative effects like tunnelling do not show up, because any effect that goes to zero ...
6
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5answers
850 views

Why does an electron react differently to a virtual photon in the interaction between two electrons and between an electron and a positron?

For the interaction between, say an electron and a positron, there correspond many (infinite) Feynman diagrams with well described mathematical expressions for the incoming and outgoing particles and ...
8
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3answers
1k 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 \delta_Z(\partial_\mu\phi_r)^2-\frac12\...
14
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3answers
11k views

What's the difference between t-channel and s-channel in particle physics

As the Feynman diagram shows above. Does the s-channel and t-channel stands for exactly same reaction or they have big difference?
5
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2answers
842 views

Why are derivatives in interaction terms treated differently from derivatives in the kinetic term?

I know that derivative couplings in a Lagrangian interaction, such as $$\mathcal{L}_{int} = \lambda \phi (\partial_{\mu}\phi)(\partial^{\mu}\phi)$$ bring down two momentum factors into the matrix ...
4
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1answer
2k views

Scattering Processes in Scalar Yukawa Theory

I'm trying to compute nucleon-nucleon scattering in scalar Yukawa theory. Here we view a nucleon as a complex scalar field $\psi$ and a meson as a real scalar field $\phi$. They interact through $H_I=...
5
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1answer
302 views

Combinatorics geometric series two-point function

In this answer Proof of geometric series two-point function it is said: Now what about the coefficients in front of each Feynman diagram? Due to the combinatorics/factorization involved it ...
4
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3answers
560 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 ...
2
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1answer
568 views

Arrow and flow of charge in fermion propagator

The momentum-space fermion propagator in the free Dirac theory is given by The arrow on the fermion propagator is said to represent the flow of charge. How can we derive this statement ...
5
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2answers
2k views

$\phi^{4}$ Propagator - Feynman Diagram: internal vertex that loops back to itself

In all that follows I'll be dealing with everything massless. The free, massless propagator ($\mathcal{L} = \int d^{4}x \left(\partial \phi(x) \right)^{2} $) is supposedly given by $G_{0}(x,y) = c (x-...
3
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2answers
1k views

Symmetry factor via Wick's theorem

Consider the lagrangian of the real scalar field given by $$\mathcal L = \frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{4!} \phi^4$$ Disregarding snail contributions, the ...
3
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2answers
591 views

Does path integral and loop integral in a Feynman diagram violate special relativity?

Consider a correlation function between two points $A(x_1,t_1)$ and $B(x_2,t_2)$, we need to integrate over paths which could be infinite long. But the time length $(t_1-t_2)$ is finite, so if $A$ and ...
3
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3answers
636 views

How does a photon “know” that it's left one charge and that it's going to another one?

How does it know the same charge it left will be the same charge it will return to? My understanding is photons are neutral and have no charge. i.e. Like charges repel, unlike attract. All charged ...
2
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1answer
4k views

Neutrino-Neutron Interaction Feynman Diagram (W Boson Direction)

I am currently studying differential cross sections for my Nuclear Physics module. I'm looking an experiment where muon-neutrinos are interacting with nucleons in a scintillator producing muons (which ...
4
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2answers
677 views

How to calculate the tree-level probability amplitude for the electron-positron to muon-antimuon process?

Consider the following process: $e^+ + e^- \rightarrow \mu^+ + \mu^-$. I'm trying to calculate the probability amplitude of such a process in leading order. In leading order the amplitude is given by:...
3
votes
1answer
875 views

Fourier transform of the free propagator squared - $\int d^{4}p\ \frac{e^{-i p\cdot x}}{p^{2}+m^{2}-i\epsilon}$

The point of the question is to ask what is the function given by the following integral: $$ H(x,y) \ \equiv \ \int \frac{d^{4}p}{(2\pi)^{4}} \frac{e^{-i p \cdot (x-y)}}{(p^{2}+m^{2}-i\epsilon)^{2}} $$...
2
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0answers
128 views

Calculation of Feynman invariant amplitude with internal global symmetry indices: trace over\and isospin

This is a complete rewriting of the older post, making more clear the problem. The issue here is to compute the $$|M|^2 =4a^2(\delta_{ad}\delta_{bc} - \frac{1}{2} \delta_{ab}\delta_{cd}) ^2 (u_{1b}^{...
2
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1answer
304 views

How does virtual particle explanation of Hawking radiation contradict with consistent loop description?

the picture of virtual particle pairs is categorically not the right way to think about Hawking radiation. Quite obviously it must be wrong, because it is a loop level effect, and loops in QFT have to ...
0
votes
1answer
44 views

How do I find the values for the structure constants ($f^{abc}$) of a gauge group?

How do I find the values for the structure constants ($f^{abc}$) of a gauge group, as a mean to find the tree-level amplitude for a process in which one of the tree-level diagrams is: the process ...
0
votes
1answer
204 views

Geometric series for two-point function

In deriving the expression for the exact propagator $$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$ for $\phi^4$ theory all books that i know use the following argument: $$G_c^{(2)}(x_1,x_2)=G_0^{(2)}...
22
votes
1answer
3k 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 ...
8
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1answer
2k 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 ...