"The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known". Since it includes electromagnetism, at least an aspect of the model has a classical limit, namely Maxwell's equations. Is this the only aspect of the model that has a defined classical limit?
59922
Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
117121
I am looking for a preferably introductory text on Yang-Mills theory with mathematical basis and language. (Differential forms) I have a background in QCD and QED, however, I want to go more in details in geometrical interpretations of Yang-Mills theory. I am sorry if this question has asked before. Thanks in advance.
112981
Electricity and magnetism was unified in the 19th century, and unification of electromagnetism with the weak force followed suit, bringing into play the electroweak force.  I've been told that unifying these with the strong force is likely to be far easier than unifying them with gravity, albeit still very hard.   Apparently this is because of the fact that electromagnetic, weak nuclear and weak nuclear force equations are relatively similar, whereas the equations for gravity differ greatly.  What are the fundamental differences between these equations? (If you could write some that would be great, and then explain the technical differences, if necessary.)  What is it about these differences that make them much harder to unify?
13321
This is a rather broad question. Does anyone know of good video lectures for graduate level classical electrodynamics?
65939
If photons are spin-1 bosons, then doesn't quantum mechanics imply that the allowed values for the z-component of spin (in units of $\hbar$) are -1, 0, and 1?  Why then in practice do we only use the $\pm 1$ states?  I have been told that this is directly related to the two polarizations of the photon.  This seems to be more of a classical argument however, arising from the fact that Maxwell's equations do not permit longitudinal EM waves in a vacuum.  I have also heard that it is related to the fact that photons have no rest mass, although I understand far less of this reasoning.  What I'm looking for are elaborations on these two arguments (if I have them correct), and perhaps an argument as to how these two are equivalent (if one exists).
54636
It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scattering in QED corresponds to scattering of classical point charges. The naive explanation for this is that the power of $\hbar$ in a term of the perturbative expansion is the number of loops in the diagram.  However, it is not clear to me how to state this correspondence in general. In the above example the classical theory regards electrons as particles and photons as a field. This seems arbitrary. Moreover, if we consider for example $\phi^4$ theory than the interaction of the $phi$-quanta is mediated by nothing except the $phi$-field itself. What is the corresponding classical theory? Does it contain both $phi$-particles and a $phi$-field?  Also, does this correspondence extend to anything besides scattering theory?  Summing up, my question is:     What is the precise statement of the correspondence between tree-level QFT and behavior of classical fields and particles?
12136
I am reading now E. Soper, Classical Theory Of Fields, now and sometimes it is very hard to follow the equations. So I need a side book on  to read it comfortably. Landau &amp; Lifshitz's book is not helping as its content and topics are very much different.
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I read this in my textbook: A charged particle or object is not affected by its own electric field.  Since I find this completely unintuitive and my mind is yelling "wrong! wrong! how could a particle even distinguish between its own field and the external fields?" I would really like to hear an explanation about why this is true, if it is.  (A corollary question that comes to my mind after thinking about this is... What about gravity and mass considering the analogous situation? And the other two forces?)
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This question has been touched tangentially by  and  but I do not think they reach the core of my question.  When I read that many other theories, e.g. the Standard Model, have been constructed to be Lorentz invariant it appears that electromagnetism has some of preponderant role in the universe compared to other theories. I suspect that the answer is that this is not the case, and that the space-time Speed of Light (with upper-case) is really more of a universal constant that is not necessarily related to the speed of the electromagnetic waves or of photons.  There are many other related questions:    would it really be devastating for relativity that we find out in the future that photons have a tiny mass and move slower than ... uhh... the speed of light? which "c" is applicable in different situations? I mean, possibly the space-time constant should be used in $E=mc^2\gamma$, it would be the  velocity of gravitational waves, etc..., but in other situations such as the Bohr radius or Compton wavelength I am not sure.   Well, any answer will be appreciated. Please tell me if you know any reference to bibliography that address this issue.
8239
I have came across this recent development in the LHC: Breakthrough at the Large Hadron Collider:  Leptoquarks and leptons - quarks unification:   Leptoquarks (LQs) are hypothetical particles that would interact with quarks and leptons. Leptoquarks are color-triplet bosons that carry both lepton and baryon numbers. Their other quantum numbers, like spin, (fractional) electric charge and weak isospin vary among theories.  Does this mean that we are heading for a strong-EM forces unification? Is the Electron after all coupled to the individual quarks in the nucleus via these new boson? And therefore new unifying force discovered?
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In the  of particle physics, there are three generations of quarks (up/down, strange/charm, and top/bottom), along with three generations of leptons (electron, muon, and tau).  All of these particles have been observed experimentally, and we don't seem to have seen anything new along these lines.  A priori, this doesn't eliminate the possibility of a fourth generation, but the physicists I've spoken to do not think additional generations are likely.     Question: What sort of theoretical or experimental reasons do we have for this limitation?   One reason I heard from my officemate is that we haven't seen new neutrinos.  Neutrinos seem to be light enough that if another generation's neutrino is too heavy to be detected, then the corresponding quarks would be massive enough that new physics might interfere with their existence.  This suggests the question: is there a general rule relating neutrino masses to quark masses, or would an exceptionally heavy neutrino just look bizarre but otherwise be okay with our current state of knowledge?  Another reason I've heard involves the Yukawa coupling between quarks and the Higgs field.  Apparently, if quark masses get much beyond the top quark mass, the coupling gets strong enough that QCD fails to accurately describe the resulting theory.  My wild guess is that this really means perturbative expansions in Feynman diagrams don't even pretend to converge, but that it may not necessarily eliminate alternative techniques like lattice QCD (about which I know nothing).  Additional reasons would be greatly appreciated, and any words or references (the more mathy the better) that would help to illuminate the previous paragraphs would be nice.
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I am assuming there are two constituents that obliterate our current model of physics;   that it's infinitely dense that it's infinitely small   Please correct me if I am wrong.
24153
Consider the question, .  The answers say, "an elementary particle" and not much else. They don't actually answer the question. Moreover, the question is flagged as a duplicate of,  &ndash; the answers there don't tell me what a photon is either. Nor do any of the answers to  mentioned in the comments. When I search on , I can't find anything useful. Questions such as,  look promising, but bear no fruit.  say things like, "the photon is an excitation of the photon field." That tells me  nothing. Nor does the , which says:     The photon is the quantum of the electromagnetic four-potential, and therefore the massless bosonic particle associated with the electromagnetic force, commonly also called the 'particle of light'...   I'd say that's less than helpful because it gives the impression that photons are forever popping into existence and flying back and forth exerting force. This same concept is in the  too - but it isn't true. As , "Virtual particles only exist in the mathematics of the model." So, who can tell me what a real photon is, or refer me to some kind of authoritative informative definition that is accepted and trusted by particle physicists? I say all this because I think it's of paramount importance. If we have no clear idea of what a photon actually is, we lack foundation. It's like what :     Photons seem to be one of the foundation ideas of quantum mechanics, so I am concerned that without a clear definition or set of concrete examples, the basis for understanding quantum experiments is a little fuzzy.   I second that, only more so. How can we understand pair production if we don't understand what the photon is? Or the electron? Or the electromagnetic field? Or everything else? It all starts with the photon.   I will give a 400-point bounty to the least-worst answer to the question. One answer will get the bounty, even if I don't like it. And the question is this:    What exactly is a photon?
105813
So in my textbook, it states that the $E=hf$ equation applies to electrons, and all particles, not just photons.   But in order to prove this, wouldn't these particles need to have zero mass, to satisfy $E=pc$ from Einstein's equation?  In Einstein's theory of relativity $E^2= p^2c^2 + m^2c^4$, we get $E=pc$ because we consider the mass to be zero.   For $E=hf$ to work for other particles, don't we need to assume electrons have zero rest mass?
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In his  Feynman calculates the field momentum of a moving charged sphere with charge $q$, radius $a$ and velocity $\mathbf{v}$. He finds that the total momentum in the electromagnetic field around the charged sphere is given by:  $$\mathbf{p} = \frac{2}{3} \frac{q^2}{4\pi \epsilon_0} \frac{\mathbf{v}}{ac^2}.$$  He calls the coefficient between the field momentum, $\mathbf{p}$, and the velocity, $\mathbf{v}$, the electromagnetic mass:  $$m_\textrm{elec}=\frac{2}{3} \frac{q^2}{4\pi \epsilon_0 a c^2}.$$  He claims that this electromagnetic mass $m_\textrm{elec}$ has to be added to the standard "mechanical mass" of the sphere to give the total observed mass of the object.  Would this view be accepted by most physicists today?  Have any experiments been performed that show the effect of the additional electromagnetic mass on the dynamics of a macroscopic charged object?  I guess the problem is that such an effect would only be large enough to be observable for charged particles like electrons. In that case it would be difficult to distinguish mechanical mass, presumably due to the Higgs field, from electromagnetic mass. Maybe one could perform a high energy/short length scale experiment on an electron that excluded the effect of the electromagnetic mass?
66161
Are there any fundamental rules of thumbs that can be used to identify the type of force interaction (weak, electromagnetic, strong) in a particle decay without drawing the Feynman diagrams at the beginning of the problem. At least to rule out some types of forces from a given decay reaction, before start drawing the Feynman diagrams.
23053
The Higgs boson and gluons have no electric charge and photons couple to charge, so there is no tree level interaction between them and photons.  But what prevents higher order diagrams from contributing a non-zero mass term to the photon, for instance    where a photon couples to some fermion (say an electron, or a top quark) which can interact with the Higgs field.   Or consider that same diagram but with quarks and a gluon interacting between them? Or any higher diagram with even more loops?  I have heard charge conservation depends on gauge invariance, which in turn depends on photons being massless.  So it appears the photon has no mass, and these diagrams must all cancel somehow.  So I'm hoping there is a very nice symmetry explanation for why they all disappear, but if I say "because of gauge invariance" that would be circular logic, so there must be another symmetry at stake here?     What prevents photons from obtaining a mass from high-order self-energy loop diagrams?