52

When we say that the forces were unified, we mean that the interaction was described by a single gauge group. For example, in the original grand unified theory, this group was $SU(5)$, which spontaneously broke down to $SU(3) \times SU(2) \times U(1)$ as the universe cooled. These three components yield the strong, weak, and electromagnetic forces ...


20

Charge conjugation is extremely slippery because there are two different versions of it; there have been many questions on this site mixing them up (1, 2, 3, 4, 5, 6, 7, 8, 9), several asked by myself a few years ago. In particular there are a couple arguments in comments above where people are talking past each other for precisely this reason. I believe ...


15

I think you have understood it almost well. The masses do not change, they are what they are; at least at colliders. At high energy, it is true that the impact of masses and, more generally, of any soft term, becomes negligible. The theory for $E\gg v$ becomes very well described by a theory that respects the whole symmetry group. Notice that to do so ...


13

An experimentalist's answer, Our observations tell us that baryon and lepton number are conserved, within the accuracies of our experiments and observations. This means we have chosen as a standard model SU(3)xSU(2)xU(1) because in the group structure of the possible representations of all the quantum numbers assigned to the particles and resonances we ...


11

This can be explained by thinking about the coupling of fermions to the $SU(2)$ weak gauge field. Let's recap what we know Weyl fermions necessarily appear in two complex representations of the Lorentz group $L$ and $R$. Only fermions in the $L$ representation of the Lorentz group couple to the $SU(2)$ gauge field. CPT is a symmetry of the theory. Now let'...


9

Is this diquark something realistic or is it an out-dated object, i.e. ruled out by experiments? According to Are Diquarks Real? there is experimental evidence that diquarks do exist. Also from the more-recent Images of the Origin of Mass: "The modern diquark correlation is nonpointlike, with the charge radius of a given diquark being typically 10% larger ...


8

It should perhaps be stressed that the magnetic monopoles that many GUTs predict are generalized 't Hooft Polyakov monopoles (as opposed to e.g. the Dirac/Wu-Yang monopoles, which are singular in a point/exclude a point). Once a GUT action $S[A,\phi,\psi]$ is adapted, then the 't Hooft Polyakov monopoles do in principle not constitute a new independent ...


8

Actually the Lie group $$G:=SU(3)\times SU(2) \times U(1)$$ is not a subgroup of $SU(5)$. However the standard model gauge group $G/\mathbb{Z}_6$ is a subgroup of the GUT gauge group $SU(5)$, cf. e.g. this, this & this Phys.SE posts. Here we will argue at the level of Lie algebras $$su(3)\oplus su(2) \oplus u(1)\subseteq su(5).$$ In detail, we identify ...


7

First of all, the big desert hypothesis isn't in contradiction with – isn't a competitor of – the seesaw mechanism for neutrino masses. Quite on the contrary, assuming a big desert between the electroweak scale and the GUT scale is the most natural way to be sure that the small seesaw terms in the neutrino masses are the dominant ones that matter. The seesaw ...


7

In the standard model lagrangian, B and L are separately conserved global charges, and B-L, a vector like symmetry, is anomaly-free. GUTs, like the G-G SU(5) violate B and L, but preserve B-L. Wikipedia effectively defines the SU(5)-model U(1) symmetry X as $$X = 5(B − L) -2Y_W, $$ introduced by Wilczek & Zee in 1979. It is not a generator of SU(5), ...


6

Actually, $$G~:=~SU(3) \times SU(2)\times U(1)$$ is not a subgroup of $SU(5)$, but $G/\mathbb{Z}_6$ is a subgroup of $SU(5)$, cf. e.g. this Phys.SE post and Ref. 1. We interprete OP's question (v3) as essentially asking Is $G/\mathbb{Z}_6$ a normal subgroup of $SU(5)$? Or in terms of the corresponding Lie algebras, Is $su(3) \oplus su(2)\oplus u(...


6

"Unification" refers to explaining two sets of phenomena (theories) which were previously urelated, and combining them into a single cohesive description. Eg: electricy and magnetism unified into electromagnetism. While those two sets of phenomena could be approximately treated (in one regime) by neglecting the other, it is important that the two ...


5

As very well known, the root lattice $Q$ of a semisimple Lie group is a sub-lattice of its weight lattice $P$ because the roots are the weights of the adjoint representation. The congruence class of a weight (which is the generalization of the triality in $SU(3)$) is its representative in the coset $P/Q$. (Slansky calls it "congruency class"). In this ...


5

Assume You have only $C$-violation. Then it implies that the rate $\Gamma$ of hypothetical process $p^{-} \to e^{-}\gamma$ won't be equal to the rate of hypothetical process $p^{+} \to e^{+}\gamma$, but only for the given helicities $L/R$. Say, $$ \tag 1 \Gamma\big(p_{L}^{+} \to e^{+}_{R}\gamma_{L}\big) \neq \Gamma(p_{L}^{-} \to e^{-}_{R}\gamma_{L}), $$ and $...


4

Is the observation of only one Higgs and no supersymmetric particle below 8 TeV (up to now) a sufficient evidence to substantiate the almost commutative spectral model? No, absolutely not. The Chamseddine-Connes model assumes the existence of a desert, with no new field excitations or strong coupling phenomena between the 1 TeV scale and the GUT scale, ...


4

The experimental evidence comes from the running coupling constants. One important clue that they (couplings) might all be the same comes from the fact that the coupling constants are not constants at all. Instead, they vary with the energy of the phenomenon in which they are measured. The value of as quoted above is only true for phenomena that occur at ...


4

My suggestion, don't waste your time on it. Only from this Not only does the helical particle wave concept explain all the characteristics of light, etc., by means of a single model, but it allows one to calculate the exact position, velocity and spin of any relativistic particle without the need for such dubious concepts as: Einstein's time dilation and ...


4

I think that there are at least two things that might not work for these models. The first would be if they don't give rise to the right abundance, e.g. not enough is produced before the particles decouple from the plasma. The other issue is (even providing the right amount) the cold dark matter particle is cold (non-relativistic) enough not so spoil the ...


4

Ref. 1 does not seem to mention a symmetry-breaking $U(1)$ that belongs to the part of $SU(5)$ that is not in the standard model. In this answer, we will assume that OP is really asking about the weak hypercharge $U(1)$ gauge factor of the standard model. At the Lie algebra level, recall that the Lie algebra $su(n)$ consists of Hermitian traceless $n\times ...


4

The answer to your question requires some knowledge on group theory and tensor analysis, but I will try to make it as simple as possible with out going into too much of technicalities. Your question consists of basically two completely disjoint parts, they are: why the gauge bosons(leptoquarks) of Pati-Salam Group do not mediate proton decay. Which is a ...


4

If you don't impose some sort of simplicity restriction on the grand unified group, then the Standard Model gauge group $\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)$ would already classify as a GUT group, making the search for a GUT pointless. There is no problem as such with non-simple gauge groups, but they just don't correspond to what we call "...


4

From your link: Dirac came out of his depression when he received a phone call from his friend Abdus Salam, saying: "Relax Paul, my friend Nino Zichichi has discovered the antideuteron". This is the opposite of the summary in your question (v1) which suggests that Dirac believed for some reason that the antideuteron shouldn't occur and was upset when it ...


4

Amateur would-be physicists (and quite a few professional physicists) have discovered many mathematical formulas for the unexplained constants of the standard model, such as for the fine structure constant (approximately equal to 1/137). These will be expressions involving e, pi, natural numbers, square roots, and so on, in some combination. This is often ...


4

Yes, there is a representation-theoretic way to do this in one step. Zee is taking a slightly different approach, showing the cancellation of the $U(1)^3$ anomaly where $U(1)$ is the hypercharge subgroup of the SM gauge group embedded in $SU(5)$. But actually it's easier to do the whole calculation in one go, looking at the whole gauge group $SU(5)$. We ...


4

That section of the wikipedia page first appeared in a 2017 paper from vixra. It's the jargon of one person's private theory of everything, and not something you would see in a textbook.


4

You've got a misunderstanding. The grand unification energy of $10^{16}$ GeV is meant as an energy of a single particle. But the solar radiation ($1.74 \cdot 10^{17}$ J/s) is the energy of many photons. A single solar photon has an energy of only a few eV. By the way: Even the particle energies achieved with our most powerful accelerators (like the LHC) ...


4

I think this is a perfect storm of confused notations, where absolutely every misread symbol of WP is thrown on the fire. To alleviate confusion, I'll skip SO(10) completely, stick to SU(5), and use different symbols for the charges and the gauge bosons. The short answer is that the twelve $\mathbb{X}$ and $\mathbb{Y}$ gauge fields and their corresponding ...


4

I don't know where that "we" came from, but the SM "unification" is partial, more of a Weinberg-angle tilt: It involves EM and WI inextricably linked and mixed. The different masses of W and the Z mirror the two couplings. For vanishing Weinberg angle, there would be no mixing and e=g'. The question then is just a matter of terminology, ...


3

While the answer provided above is correct, there's maybe simple / less technical way to see this. I put it here hoping it would help other curious minds. In any gauge theory based on a simple non-abelian group, gauge bosons mediate interactions between (i.e., connect) particles belonging to the same multiplet (example: in the SM, the fact that charged ...


3

Unification in physics is used differently in classical physics than in the quantum regimeof elementary particles. Unifying electricity and magnetism became necessary when functional measured relations appeared which connected the motion of charges with the magnetic field and the magnetic field with the motion of charges. The Biot-Savart law and Ampere's ...


Only top voted, non community-wiki answers of a minimum length are eligible