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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 ...

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

:-) 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 ...

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, ...

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.

7

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".

6

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 ...

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 ...

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

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 ...

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 ...

5

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 ...

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 ...

4

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 $f_{abc}$ ...

4

Feynman diagrams are just that: diagrams. Real or virtual is what the particles depicted in them can be. A distinction should be made: In order to calculate an amplitude, one needs to integrate over all possible momenta of internal lines. Therefore, those propagators can be thought as virtual. Effectively, one sums over all virtuality levels of the internal ...

4

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 ...

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 ...

4

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 ...

4

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 ...

4

That looks correct to me. Consider the basic property of the delta functions $$\int dx f(x) \delta(x-a) = f(a).$$ Nothing forbids $f(x)$ to be a composite function, for example $f(x) \equiv g(x)\delta(x-b)$, so $f(a) = g(a) \delta(a-b)$. Hence we get, $$\int dx f(x) \delta(x-a) \equiv \int dx \, g(x)\delta(x-b) \delta(x-a) = g(a)\delta(a-b).$$

4

The only argument I can find for this is a couple pages earlier, where they say ...which in turn implies that the photon self-energy diagrams have the structure $= i(q^2 g^{\mu\nu} - q^\mu q^\nu)\Pi(q^2)$ The only divergence possible is a logarithmically divergent contribution to $\Pi(q^2)$. In non-Abelian gauge theories, (16.57) still holds, ...

4

This link shows the massive calculation of the sunset diagram which is the name of the diagram you want to look at . The massless limit is simple. I suspect this question will be closed soon for being too specific and not relating to any physics concepts, though...

4

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 a shift of the vacuum: the vacuum of the interacting theory differs from that of the free field theory. Regarding your second question: strongly connected (also called ...

3

Decaying particles are described by complex energies, the imaginary part of which encodes life-time information. They are observable; in case of very short-lived particles such as the Higgs in the form of resonances, http://en.wikipedia.org/wiki/Resonance_(particle_physics) , i.e., a peak in the production rate of products of Higgs decays. The decay itself ...

3

I would like to recommend to you the following lecture notes by V.P. Nair. These lecture notes contain a very concise chapter about twistors, their relation to massless wave equations and their use in the construction of Yang-Mills amplitudes. The importance of this work to me is that, here, Nair connects these two applications to another (may be less ...

3

first of all: the unitarity method is not new. It's been known since the 60s basically and goes back to work by Cutkowsky and has been extended in work by Bern, Dixon, Dunbar, and Kowoser in the 90s. The idea is that if you cut an amplitude in two all particles will be exchanged in the cut channel. It's basically just a statement about probablities summing ...

3

The amplitudes in generic QFTs behave like $${\mathcal A} \sim \sum_{L=0}^\infty L! \cdot A_L \cdot g^{2L}$$ where $A_L$ has a slower dependence on $L$ than the factor $L!$. This fact may be obtained by counting Feynman diagrams (permutations of vertices and loops... many types of Feynman diagrams) or by solving analytically solvable examples. Because of ...

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