# Tag Info

15

Here I'll try to basically connect some dots to guide you through the example of the second text you posted... Any quantum field theory of your choice associates certain integrals to observables, which you have to compute. The Feynman diagrams are representations of these integrals. The lines correspond to propergators, which encode the different field ...

15

Ever since Newton and the use of mathematics in physics, physics can be defined as a discipline where nature is modeled by mathematics. One should have clear in mind what nature means and what mathematics is. Nature we know by measurements and observations. Mathematics is a self consistent discipline with axioms, theorems and statements having absolute ...

11

The book Quantum dissipative systems by Weiss dedicates a subsection to the Feynman Vernon method, see also the original reference. See also this article and chapter 18.8 of the book by Kleinert. It's applied to the Caldeira-Leggett model, which is a toy model for a particle in contact with a heat bath. There are a number of mesoscopic systems out there in ...

11

:-) The best gentle introduction to basic twistor theory that I know of is the book by Huggett and Tod If you don't have access to that book and some other answers don't surface in the meantime I'm happy to write a few bits and pieces here, but will have to wait until the weekend. (I may be biased, but I think it's well worth learning, as the MHV ...

11

It is not a good idea to see a Feynman diagram as some sort of collision process really happening. The diagram is just a term in the perturbative expansion of a quantum mechanical transition amplitude (in other words, a nice "graphical" way to represent a bunch of integrals). The only actual observed objects are two incoming photons with a certain energy, ...

10

Peskin and Schroeder tends to be the book used in most introductory QFT courses, so you'll definitely find all things there done in a pretty detailed way. Warren Siegel has an online book which is also pretty good, Fields.

10

The first thing to notice, as pointed out in the comments, is that time increases going up. So if you are more familiar with viewing Feynman diagrams where time increases to the right, this problem is easily solved: just rotate the diagram by 90 degrees when you are interpreting it. If the problem is that you're not all that familiar with matter lines in ...

10

Your assumption that pair production is ruled out, rules out* that two photons interact through higher-order processes. Quantum electrodynamics tells us that two photons cannot couple directly. That leaves us with classical electromagnetism, which tells us that electromagnetic waves pass through each other without any interference. *Edit. The photons can ...

10

Diagram machinery works also for perturbation theory in classical statistical mechanics and classical field theories. Generally, various kinds of diagrams constitute a pictorial way of talking about tensor products and their contractions while hiding the multi-linear algebra from the layman. In the simplest case, vertices (or blobs) represent vectors, ...

9

For nucleon-nucleon interaction please keep in mind that in this low-energy regime pertubative QCD breaks down and reactions are not really calculable. For the specific pion exchange you mention have a look at http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html as to why this QCD-process can be seen as an exchange of a pion. In general you ...

9

Drawing from Feynman's and Wheeler's memoirs: Feynman was originally motivated to produce a theory of EM without the infinities of self-interaction, but he then needed a mechanism to reproduce radiation reaction, the loss of energy of an accelerating electron. He thought that a nearby electron could back-react to achieve the effect, but his advisor ...

9

The MHV ideas are concerned, typically, with scattering amplitudes of gluons in Yang Mills theories. Most of the foundational work has been done with $\mathcal{N}=4$ supersymmetric Yang Mills theory, though I believe there have been extensions beyond this. The problem addressed is that you have n gluons meeting at a vertex, some incoming, some outgoing and ...

8

One of the avenues to search for an answer is the so-called Keldysh formalism which is used extensively in condensed matter, in particular in mescopic physics, to define and study steady-state and time-dependent quantum phenomena in systems with infinitely many degrees of freedom. A recent comprehensive review is given by Kamenev and Levchenko, ...

8

The reasons were given here. Essentially, at tree level you recover classical results. Loop corrections are proportional to powers of $\hbar$ and these are quantum terms.

8

Well, it need not be a Lagrangian, you can work in Hamiltonian formalism too (which is often possible outside of particle physics, e.g. in condensed matter theory). But except for this caveat the answer is a resounding yes: the theory comes first and diagrams are just mnemonics. Diagram by itself doesn't make any sense if you can't reconstruct the ...

8

There are, of course, a lot of codes floating around. Which of them you should choose, depends on what you want to calculate exactly. Here I mention four possibilities: 1) CALHEP - this package takes you from a given Lagrangian through its Feynmann rules to the calculation of cross sections. 2) xloops - this package calculates the 1-PI Feynman diagrams ...

8

The electron-positron pair can produce directly a Higgs boson, but this process is very suppressed, because the coupling between the leptons and the Higgs is proportional to the tiny mass $m_e$: $$g_{\rm Hee}=-i\frac{ m_e}{v},$$ where $v\approx 246 \,\rm{GeV}.$ On the other hand, the process $e^+ e^-\to H Z$ is more likely to happen, because the coupling ...

8

I would guess that the professor is explaining his/the(?) theory that dark matter is neutrinos, produced via a scattering process he calls "Witten's dog". It is funny because the neutrinos are coming out of the dog's butt. In the Standard Humor Classification, this is known as a "poop joke".

8

The fact that only connected Feynman diagrams contribute to the scattering amplitude can be interpreted in terms of the vacuum of the theory. Omitting disconnected diagrams amounts to shifting the vacuum: the vacuum of the interacting theory differs from that of the free theory. Regarding your second question: strongly connected (also called one-particle ...

8

This is a perceptive question. Consider the following from the Wikipedia article "Virtual Particle": As a consequence of quantum mechanical uncertainty, any object or process that exists for a limited time or in a limited volume cannot have a precisely defined energy or momentum. This is the reason that virtual particles — which exist only ...

7

Assume that the generating functional is given by a sum of all possible diagrams, i.e. $$Z(J)=\Sigma_{n_i} D_{n_i}.$$ Furthermore, assume that each diagram D is given by a product of connected diagrams $C_i$, i.e. a diagram D can be disconnected. We will write this as $$D_{n_i}=\Pi_i\frac{1}{n_i!}C_i^{n_i},$$ where dividing by $n_i!$ amounts for a ...

7

A lowest order QED Feynman diagram for the process photon + photon $\rightarrow$ electron + positron looks like shown below (the time axis is the horizontal axis). From the point of view of energy conservation, this process is only possible if sum of the energy of the photons is above twice the electron mass. In the center of mass frame of the di-photon ...

7

My own attempt at this: the first result is wrong, and the second one is right but incomplete. Feynman: in the diagram, all the lines are external, so there is no propagator in the diagram. Therefore, Feynman rules give $\mathcal A=1$. Check up of this: In canonical quantisation, the amplitude is given by $\langle p|q\rangle=\langle 0|a_p ... 6 One of the main reasons the virtual particles are used is that in many contexts we do not have a non-perturbative formulation of quantum field theory. What we can do is compute some amplitudes perturbatively (e.g. for outcomes of particle collisions) using Feynman diagrams. These diagrams have input/output lines in them, usually identified with colliding ... 6 For instance, how did he come up with interpreting the propagator as the propagation of particles? The path integral is usually introduced as a matrix element of the time evolution operator $$\langle x_f\lvert\mathrm e^{-\frac{\mathrm i}{\hbar}\hat{H}(t_f-t_i)}\lvert x_i\rangle,$$ which is a measure of the probability of finding a system in final ... 6 I don't think that there would be any more diagrams. Having a total derivative term in the Lagrangian leads to derivative interaction vertex, which after symmetrising gives you something like $$ig \sum_i p_i \ ,$$ where$g$is some coupling and$p_i$the momenta of the particles. This vertex, however, vanishes due to momentum ... 6 At the tree level (i.e. the simplest Feynman diagram) the both types of weak interaction result from the exchange of a weak boson. The weak bosons are the$Z^0$(neutral) and the$W^\pm\$ (charged). Guess how we assign the terms "neutral" and "charged" to weak interactions. Right, by the exchange boson. (We don't distinguish between interaction involving the ...

6

Virtual particles are not real. Though sounding like a tautology, it is an important one - they are not actual states in the asymptotic Hilbert spaces of a quantum field theory, where particles usually live. They are a name given to internal lines of Feynman diagrams, which, in turn, are mere computational tools in a perturbative approach to QFT. Nothing in ...

6

In the normal usage, real and virtual are not properties of Feynman diagrams themselves, but of the particles depicted in them. The particles corresponding to external lines (attached to at most one vertex only) are real, the others (attached to two vertices) are virtual. A Feynman diagram may be considered as a repetitive part of a bigger diagram. This ...

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