# Tag Info

8

Yes there are "virtual" Higgs bosons. A virtual particle isn't really a particle but a ripple / disturbance in a field. So a virtual electron is a ripple in the electron field. A virtual higgs is a ripple in the higgs field. Virtual particles are just a convenient conceptual model for describing field disturbances in terms of particles. Matt Strassler ...

7

Note carefully Nick's comment. Suppose I send two plane EM waves on some collision course so they interfere. The waves will pass through the region where they meet, generating some interference pattern in that region, then they will exit that region and continue on their separate ways unchanged. In other words neither the energy nor the momentum of the waves ...

5

Another way to say this: Speed of photon, graviton, gluon all equal to c? or Whether all massless particles necessarily have the same speed? You must not have been introduced to the concept of a virtual particle: In physics, a virtual particle is a transient fluctuation that exhibits many of the characteristics of an ordinary particle, but that ...

4

I suppose you talk about the standard $2\pi$ that appears in the rules for Fourier transform. The factor of $2\pi$ or $1/2\pi$ or two factors of $1/\sqrt{2\pi}$ have to appear "somewhere" in the Fourier transform rules because this is what the mathematics implies. At any rate, if this is your question, it is a mathematical question and you may learn it in ...

4

I) The meaning of the word on-shell depends on context. We are aware of at least three meanings. The original meaning of the word on-shell refers to (as Lubos Motl writes in his correct answer) that the mass-shell condition $$p_0^2 - p_1^2-p_2^2-p_3^2 ~=~m_0^2$$ is satisfied for a 4-momentum $p_{\mu}\in \mathbb{R}^4$. The mass-shell is therefore a ...

3

The Klein Gordon field as you've written it actually isn't conformally invariant for $D\neq 2$. (It is, classically, scale invariant, but it isn't Weyl invariant. Quantum mechanically even the scale invariance is broken.). To get a conformal field theory you need to include the so-called "conformal coupling" to gravity. This will change the number of ...

3

There is no need for high order mechanism. It is simply because a single photon can interfere with itself. If you remember the double slit experiment, they are indeed looking for a single photon passing through a slit and interfere with itself. Now if, instead we have billions of billions photons, the same single photon interference still happen ...

3

If basic symmetry and homogeneity assumptions about the Universe hold, then yes, all massless real particles (see Anna V's answer for virtual particles must travel at a universal constant $c$, the speed of a massless particle, in all frames of reference. Given these basic symmetry and homogeneity assumptions, one can derive the possible co-ordinate ...

3

I think the answer is it depends on distance (relative to the size of your system). Another well known example of a boson which is comprised of fermionic components is the helium-4 atom, which has integer spin (both the nucleus and the neutral atom itself). Fermionic or bosonic behavior of a composite particle (or system) is only seen at large (compared ...

2

Both $\mathbb{R}^3$ and $S^3$ are rank 1 symmetric spaces explicitly, as a homogeneous spaces they are given by: $$\mathbb{R}^3 = ISO(3)/SO(3)$$ and $$S^3 = SO(4)/SO(3)$$ The significance of their being rank-1 symmetric spaces is that there is only one "two-point" invariant on them, i.e., any function of two points $r_1$ and $r_2$ invariant under the ...

2

The observables of the theory are, first of all, those in the algebra $\cal A$ (technically a $^*$-algebra with unit) of objects generated by the smeared fields $\phi(f)$. I mean linear combinations of $I$ and products of smeared fields $\phi(f)$, where $f$ is a complex valued compactly supported smooth function. This algebra can be enlarged by including ...

2

As Trimok said, the probability of scattering of some nicely focused packets will still go like the cross section and like $|{\mathcal M}|^2$. For bosons, there are no energy-dependent extra factors, so $|{\mathcal M}|^2$ itself has to be smaller than a number of order one for the probability to stay smaller than one. This is related to $T^\dagger ... 1 Suppose$A$is at the space-time origin$0$, and$B$is at space-time event$x$. You suppose that a real photon could go from$A$to$B$, so this means that$A$and$B$are separated by a light-like interval, that is$x^2 = (x^0)^2- \vec x^2=0$. This means that$x^0>0$, too. Now, the propagator$D_{\mu\nu}(x)$represents the amplitude for a photonic ... 1 The nLab is a great reference for all of these things and seems to answer all of your questions. They do a better job of explaining why than I would probably do. Their page on Chern-Simons Theory seems to answer questions (2)-(4). They give a method for constructing Chern-Simons theories from generic compact Lie groups in the page listed. They also have a ... 1 Virtual particles made their appearance when Feynman diagrams came to life. A working definition is that a virtual particle is an internal line in a Feynman diagram : its four vector is not constrained by the mass of the particle, it is an off mass shell four vector carrying all the other quantum numbers of the particle. That is why one speaks of "off mass ... 1 If you have a scattering event with particles going IN and OUT, so we send the IN particles and measure the OUT particles. A virtual particle is just any particle contributing to the event which isn't in the IN or OUT state, i.e. it is created and destroyed during the event. The reason particles like this can exist is due to quantum fluctuations of the ... 1 I think there is a long list of things we know about but don't understand yet. For example, we know neutrinos have mass but we don't yet know what those masses are or even exactly how they acquire mass (but it's probably the Majorana process). There is a long list of things that we're still trying to figure out but that's not the central part of my point. ... 1 When beginning by calculate transition amplitudes in position space, and taking the Fourier transform of these amplitudes, to get the transition amplitude in momentum space, you get terms (for instance in a$2 \to 2$interaction) in$\int d^4v e ^{-i(p_1+p_2-p_3-p_4)v}$, and this is equals to$(2\pi)^4 \delta^4(p_1+p_2-p_3-p_4)$An example of such an ... 1 I thought the same thing for a long time. I wondered why gluons don't fly out of the nucleus at the speed of$c\$. The difference is that photons don't interact with other photons and gravitons don't interact with other gravitons. They can move around and pass through each other. On the other hand, gluons do interact with each other. In fact, gluons form ...

1

I can answer (1) and (2). The answer is: NO. Passing form classical mechanics to quantum one requires, in general, to add more information. There is no rigorous machinery allowing one to write the quantum corresponding of a classical object. Physically speaking, this is because quantum structures are more fundamental in Nature than classical ones. ...

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