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18

The main important idea of Feynman Wheeler theory is to use propagators which are non-causal, that can go forward and backward in time. This makes no sense in the Hamiltonian framework, since the backward in time business requires a formalism that is not rigidly stepping from timestep to timestep. Once you give up on a Hamiltonian, you can also ask that the ...


10

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 ...


10

:-) 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 ...


10

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 ...


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

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 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

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

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 ...


7

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 ...


7

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.


6

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 ...


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 ...


6

If I understand your question correctly its just a matter of what you are calculating whether you put the external particles on shell or not. If you are, for example, calculating an amplitude to use for a cross section, you'll put the external particles on-shell and it will be what you call a 'real Feynman diagram'. If you are calculating an effective action ...


6

The main purpose of the space and time dimensions in Feynman diagrams is that the space dimension represents all possible spacial dimensions. 3D plots (which I assume you mean give two dimensions to space and one to time) would really only serve to give extra space on the diagram for interactions that would otherwise not fit on the page or become unreadable ...


6

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 ...


6

The first process corresponds to $e^{-}e^{+}\to e^{-}e^{+}$ (Bhabha scattering), where the final and initial states are the same, consisting of an electron and positron. However, the second process is $e^{-}e^{+}\to \gamma \gamma$, where instead the final state is that of two photons. The scattering amplitudes will be different. Notice that the first diagram ...


6

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 ...


6

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 ...


5

To explain what Srednicki is doing: $C_i$ labels the connected diagrams with symmetry factors associated with them (individual diagrams) included, $n_i$ represents the number of diagrams $C_i$ present in the disconnected diagram $D$ and $S_D$ is an extra symmetry factor for the entire disconnected diagram due to interchange of lines between different ...


5

In the first case, the vertex is a vertex in the common sense (used to construct diagrams). In the second case, the gauge field is not dynamic (in a path integral formulation, you do not integrate over), it is a background field that is fixed. In that case, we are interested on the effect of this non-dynamical field on the electron field. This is useful to ...


5

The goal is to find the single particle propagator in the presence of interactions. This propogator will be the sum of all diagrams which have two external vertices. This sum of diagrams would be difficult to compute, but it turns out it easy to write this big sum of diagrams in terms of a sum of a smaller set of diagrams: the set of "one particle ...


5

The $^*$ notation does not mean excited in this case, it means "off shell" (i.e. virtual or having the "wrong" mass). At the second vertex the $Z^0$ is put "on-shell" by the emission of a Higgs (note, however, that it will decay very quickly in any case). The lepton pair can annihilate directly to the Higgs, but the event is experimentally identical to ...


5

First of all, let me comment on the "gravity + QFT" statement. For sufficiently small curvatures, where we can neglect the effects of quantum gravity, we can treat excitations of gravitational field as normal spin-2 particles. Exactly in this spirit the field of QFT in curved space was created. This theory describes well the interactions of ordinary ...


5

In the case of equal masses, there is an analytical solution (of this diagram known by the name "the two loop sunrise diagram" for the obvious reason) in terms of hypergeometric functions given by O.V. Tarasov (equation 4.32). There is also a numerical method given by: Pozzorini and Remiddi. In the case of unequal masses Müller-Stach, Weinzierl and Zayadeh ...


5

I think you are misinterpreting the statement that "it doesn't have any effect". This statement doesn't mean that the Faddeev-Popov methodology "doesn't work", as you wrote later. Instead, it means that it is completely unnecessary. If you look at the Faddeev-Popov ghosts' Lagrangian, you will see that for Abelian groups, the structure constants $f_{abc}$ ...


5

It's correct that you only replace the denominators $1/(p^2-m^2+i\epsilon)$ by $-2\pi i \delta(p^2-m^2)$ in the propagators to compute the discontinuities. The fermionic propagators must first be rewritten so that they contain the denominator I just mentioned. You're right that the numerator isn't affected in the Cutkosky rules. In some formal sense, you ...


5

Let's consider the scattering of four (two to two) open strings, for the sake of concreteness. Using Feynman's approach to quantum mechanics in terms of the sum over histories, string theory commands us to compute the tree-level diagram as the sum over all histories – world sheets – where two initial open strings become two other open strings. By conformal ...


4

What you're showing are diagrams that contribute to the two-point function/propagator of the electron. Essentially these are so-called loop corrections to the electron self-energy, which plays an important role in the renormalisation of QED. If you organise the calculation properly, then these diagrams encode how the physical mass of the electron depends on ...



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