What is actually being conserved? I've calculated it for the Wess-Zumino model but I still have no idea what is actually being conserved due to Noether's Theorem.  There is already a , but the answers don't actually say if there is anything physically conserved.  I have heard that the number of fermions is kept equal to the number of bosons, but is this not a fact that susy requires? I feel like it doesn't actually come from the charge itself.  In Qmechanic's answer it is said that "the experimental consequences of a conserved supercharge are extracted by other indirect means." What are these means?
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What is actually being conserved? I've calculated it for the Wess-Zumino model but I still have no idea what is actually being conserved due to Noether's Theorem.  There is already a similar question,  But the answers don't actually say if there is anything physically conserved.   I have heard that the number of fermions is kept equal to the number of bosons, but is this not a fact that susy requires? I feel like it doesn't actually come from the charge itself.  In Qmechanic's answer it is said that "the experimental consequences of a conserved supercharge are extracted by other indirect means." What are these means?
10946
Are there any massless (zero invariant mass) particles carrying electric charge?  If not, why not? Do we expect to see any or are they a theoretical impossibility?
27511
What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu f_i - \eta^{\mu\nu}\mathcal{L}$$ (the four conserved Noether currents corresponding to four possible spacetime translations)  where $\{f_i\}_{i=1}^N$ are the $N$ matter fields in the theory, and we assume $f_i\mapsto\alpha^\nu\partial_\nu f_i$ for translations,  and stress-energy tensor from the Einstein-Hilbert action, which is: $$ T_{\mu\nu}\equiv-\frac{2}{\sqrt{-g}}\frac{\delta\mathcal{L}_{Matter}}{\delta g^{\mu\nu}} $$   In particular, how do you get that the two are equal (are they?) for Minkowski space, for which there is no variation in the metric?
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I've seen this claim made all over the Internet.  It's on Wikipedia.  It's in John Baez's FAQ on virtual particles, it's in many popular books. I've even seen it mentioned offhand in academic papers.  So I assume there must be some truth to it.  And yet, whenever I have looked at textbooks describing how the math of Feynman diagrams works, I just can't see how this could be true.  Am I missing something?  I've spent years searching the internet for an explanation of in what sense energy conservation is violated and yet, I've never seen anything other than vague statements like "because they exist for a short period of time, they can borrow energy from the vacuum".  The rules of Feynman diagrams, as I am familiar with them, guarantee that energy and momentum are conserved at every vertex in the diagram.  As I understand it, this is not just true for external vertices, but for all internal vertices as well, no matter how many loops deep inside you are.  It's true, you integrate the loops over all possible energies and momenta independently, but there is always a delta function in momentum space that forces the sum of the energies of the virtual particles in the loops to add up to exactly the total energy of the incoming or outgoing particles.  So for example, in a photon propagator at 1-loop, you have an electron and a positron in the loop, and both can have any energy, but the sum of their energies must add up to the energy of the photon.  Right??  Or am I missing something?  I have a couple guesses as to what people might mean when they say they think energy is not conserved by virtual particles...  My first guess is that they are ignoring the actual energy of the particle and instead calculating what effective energy it would have if you looked at the mass and momentum of the particle, and then imposed the classical equations of motion on it.  But this is not the energy it has, right?  Because the particle is off-shell!  It's mass is irrelevant, because there is no mass-conservation rule, only an energy-conservation rule.  My second guess is that perhaps they are talking only about vacuum energy diagrams, where you add together loops of virtual particles which have no incoming or outgoing particles at all.  Here there is no delta function that makes the total energy of the virtual particles match the total energy of any incoming or outgoing particles.  But then what do they mean by energy conservation if not "total energy in intermediate states matches total energy in incoming and outgoing states"?  My third guess is that maybe they're talking about configuration-space Feynman diagrams instead of momentum-space diagrams.  Because now the states we're talking about are not energy-eigenstates, you are effectively adding together a sum of diagrams each with a different total energy.  But first, the expected value of energy is conserved at all times.  As is guaranteed by quantum mechanics.  It's only because you're asking about the energy of part of the superposition instead of the whole thing that you get an impartial answer (that's not summed up yet).  And second... isn't the whole idea of a particle (whether real or virtual) a plane wave (or wave packet) that's an energy and momentum eigenstate?  So in what sense is this a sensible way to think about the question at all?  Because I've seen this claim repeated so many times, I am very curious if there is something real behind it, and I'm sure there must be.  But somehow, I have never seen an explanation of where this idea comes from.
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I have a problematic question for which I have been unable to attain a satisfactory answer. What is  truly?   -  I have read about how potential energy can be seen as the "highering" of an object within a field, be it gravitational, electromagnetic, etc.   In a way, an object is lifted to a higher position, and when it eventually falls down again energy is released back.  The object does not even have to be "lifted" beforehand, as with the case of asteroids.   However, since energy cannot be destroyed, it must somehow be stored, yet how does energy truly store itself within a field? It seems hard for me to grasp that energy can physically be stored within the positioning of an object?  I can't really get my head around how a field conserves energy within it. Kinetic energy on the other hand, can be, for me, intuitively understood, as the object really is "moving" and energy manifests itself through motion.  Can anyone elaborate on this, perhaps give reasoning as to why a field can in fact "store" energy? Please point out any fallacious or naive views I seem to hold.
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For an infinite line charge, $E$ falls off with $1/r$; for an infinite sheet of charge it's independent of r! The infinitesimal contributions to $E$ fall off with $1/r^2$, so why doesn't the total $E$ fall off the same way for the infinite line and sheet charges?
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How to prove conservation of electric charge using  according to classical (non-quantum) mechanics?  I know the proof based on using Klein–Gordon field, but that derivation use quantum mechanics particularly.
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If I've got an instance of a fundamental particle, how can I separate out the measurements of these four quantities?  (I think) I understand the theory behind them, and why the particles in the standard model are predicted to have the values they do. However, the process of validation of these numbers eludes me. How have they been historically measured?
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Disclaimer: this is a homework question, so I am happy with just a hint or the expressions needed to proceed with my understanding.  I am working on the momentum conservation of a particle/anti-particle annihilation process, and I have been asked to show that the annihilation of a particle with a finite mass and its anti-particle cannot lead to the emission of only one photon.   I understand why this happens: the conservation of momentum. However, I would like show this in a more sophisticated 4-momentum proof...how would I go about showing that momentum is conserved for two photons but it is not conserved when the annihilation process creates just one photon...?  This may be a duplicate of:
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I'm looking for an example of a Hamiltonian $H$, where $H\neq T+V$, but the total energy in the system, $E=T+V$, is still conserved.   While I'm at it, I might as well add that I'd be most interested in an example from a classical field theory. Furthermore, I am looking for a nontrivial example, e.g. where $H$ doesn't just differ from $E$ by some gradient function that integrates to 0 in the action.   In particular, I am trying to get a better understanding of the physical implications of $H$ being conserved when nontrivial variables are used, i.e. physically, what does $H$ this correspond to. Conversely, can one have a system where $E = H$ in one frame, and is conserved, while in another frame $E'\neq H'$, and $H'$ is conserved while $E'$ is not?
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My physics instructor told the class, when lecturing about energy, that it can't be created or destroyed.  Why is that?  Is there a theory or scientific evidence that proves his statement true or false?  I apologize for the elementary question, but I sometimes tend to over-think things, and this is one of those times. :)
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In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously  symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of local gauge symmetry, some people says that we can formulate Higgs mechanism in a gauge invariant way, some people also says that we need only a non-zero vaccum expectation value... I am confused about this different or maybe same point of views.  In this post:  , the most highly voted answer, I still can't feel how SSB worked in Higgs mechanism. It seem that the validity of last part, the appearance of a mass term for $A$, is guaranteed if we have a non-zero equilibrium value $\phi_0$ to expand around. I do not see that the requirement that the phase of the field $\phi$ need to be fixed at some particular value to generate mass term. Thus it seems to me it is not true that SSB is really indispensable for Higgs mechanism.  To put it simply:  The spontanously breaking of what is attributed to Higgs mechanism?   local gauge symmetry global symmetry, since breaking of a "gauge symmetry" should not have any effect on physics. In higgs mechanism, the really broken symmetry is a global one. Mathematically, it is similar in looking as fixing a gauge, but one should not think it as a spontanously breakdown of local gauge symmetry. other.   Is SSB really indispensable for Higgs mechanism?    yes, Higgs mechanism is relied on the SSB of some symmetry (above question), the other approches of description eventually has spontanously broke some symmetry. No, the SSB is just one way to describe Higgs mechanism (or even not a complete way), what is really need is the non-zero vaccum expectation value, for example in the linked post the requirement for the mass term to occur is to have some non-zero expectation value of $\phi$ to expand around, we do not need the phase of the field to be fixed, thus the symmetry is not broken. Other.   some reference materials:    States that SSB of local gauge symmetry is impossible.  in the abstract states that:       gauge symmetries merely reflect a redundancy in the state description   and therefore the spontaneous breaking can not be an essential   ingredient. Indeed, as already shown by Higgs and Kibble, the   mechanism can be explained in terms of gauge invariant variables,   without invoking spontaneous symmetry breaking     In the introduction it says:      In particular, we emphasize that global U(1) phase rotation symmetry,   and not gauge symmetry, is spontaneously violated, and show that the   BCS wave function is, contrary to claims in the literature, fully   gauge invariant
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Considering that $7$ TeV is more or less the same kinetic energy as a mosquito flying, why is it considered to be a great amount of energy at the LHC?  I mean, a giant particle accelerator that can only provide 7 TeV of energy? (14 in the mass center, if I understood well). Is it because particles are so small that this amount of energy, in proportions, is then really huge?
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The electromagnet spectrum looks to be continuous, yet energy is discrete. Shouldn't one see evidence of the electron's "quantum leap"? What's going on?     Moderator, please size my photo. Thank you.
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I'm a chemist so bear with me:  I understand the  $\Delta^{+}$ and $\Delta^{0}$ to be in some sense spin (and isospin) quartet states of the proton and neutron. These can decay straight to a proton or neutron through emission of a pion, which is spin-0.  I've been puzzling about the mechanism by which this decay conserves spin. I note via Wikipedia that  into either a lepton pair or a photon pair, for which it's easy to show spin is conserved, however pion production seems to induce a loss of $J=1$.  This seems to suggest momenta of:  $\Delta^{+} (J=\frac{3}{2}) \rightarrow{} p^{+} (J=\frac{1}{2}) + \pi^{0} (J=0)$  Am I missing a boson? Is my understanding of spin flawed? I assume that if this decay exists, similar things turn up everywhere else.
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If total energy is conserved just transformed and never newly created, is there a sum of all energies that is constant? Why is it probably not that easy?
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, I claimed that there was obviously an oscillating charge in a hydrogen atom when you took the superposition of a 1s and a 2p state. One of the respected members of this community (John Rennie) , saying:     Why do you say there is an oscillating charge distribution for a hydrogen atom in a superposition of 1s and 2p states? I don't see what is doing the oscillating.   Am I the only one that sees an oscillating charge? Or is John Rennie missing something here? I'd like to know what people think.