Mordred

Not too mention all particles regardless of type contribute to CMB blackbody temperature including weakly interactive. So why aren't these SU(3) atoms detected is a very relevant question. I also noticed no one paid any attention to the SU(3) gauge I posted this involves protons and neutrons as well as mesons. Guess they don't want to think about what energy levels would be involved with those composite particles.

@JosephDavid I understand your not familiar with the mathematics so anytime I supply mathematics it doesn't relate to you as your unfamiliar with the equations. Don't worry its very common on any forum. So your in good company. My challenge has always been how do I get explanations across that don't rely on a mere matter of trust of my opinion. One might think well I could merely post articles and quote sections etc however that actually doesn't work very well. for example pertinent to what I'm going to describe below if I were to say look at equation 44 to 48 of this article on QCD superconductors comparing the QED superconductors later is I couldn't expect a large majority of our members to understand it. https://arxiv.org/pdf/0709.4635 I could for example in terms of this thread explicitly show that the Meissner effect cannot fully describe a QCD vacuum state via the mathematics. The Meissner effect specifically involves the electroweak symmetry vacuums. So here is my challenge in a nutshell a very clear distinction is the electroweak couplings as opposed to the QCD couplings for color gauge using Yang Mills and the Gell-Mann matrices. This is the electroweak couplings to Higgs field for the electroweak bosons. \[W^3_\mu=Z_\mu cos\theta_W+A_\mu sin\theta_W\] \[B_\mu= Z_\mu sin\theta_W+A_\mu cos\theta_W\] \[Z_\mu=W^3_\mu cos\theta_W+B_\mu sin\theta_W\] \[A_\mu=-W^3_\mu\sin\theta_W+B_\mu cos\theta_W\] What this shows is that the charge conjugate mediation has different coupling strengths. It also shows that the above fields are Abelian also the longitudinal components of the above is your mass terms via the energy momentum relation. Which is essentially what is also applied for the zero point energy equations longitudinal plane waves. This however is not the case in color charge mediation Which for the Miessner effect is described by BCS theory in the above (the EM/EW fields) in the above you get Cooper pairs with flux tubes providing current flow between the Cooper pairs this is true in both type 1 and type 2 superconductivity. However those flux tubes involve the E and B fields for the EM field> how that works for weak field superconductivity involves charge conjugation. Earlier I posted the charge conjugation formula. \[Q+I^3+\frac{\gamma}{2}\]. Now here is the problem with the above with color gauge. interactions (sorry this does require math) its unavoidable. a quark is described by two wavefunctions a Dirac wavefunction and a color wavefunction for the SU(3) mediation Dirac wavefunction \(\psi\) color wavefunction \(\Psi\) \[(i\gamma^\mu \partial_\mu-m)\Psi=0\] color wavefunction below \[\Psi=\psi(x)\chi_c\] the colors are below \[\chi_R=\begin{pmatrix}1\\0\\0\end{pmatrix}\] \[\chi_G=\begin{pmatrix}0\\1\\0\end{pmatrix}\] \[\chi_B=\begin{pmatrix}1\\0\\0\end{pmatrix}\] to be a gauge theory one requires invariance under Dirac invariance. (includes Lorentz invariance) \[\acute{\Psi}=e^{i g_s}{2}\alpha_j B_j(x)\Psi\] I won't bother with the mathematical proof of the last expression however the inclusion of the color gauge fields to the Dirac wavefunctions gives the Langrangian of \[\mathcal{L}=\bar{\Psi}(i\gamma_\mu D^\mu-m)\Psi-\frac{1}{4}F_{j,\mu\nu}F_j^{\mu\nu}\] with a field strength tensor of \[F^{^{\mu\nu}_j=\partial G^\mu_j-\partial^\nu_j=g_sf_[j,k,l}G_k^\mu G_l^\nu\] now what that above expression tells us is that the coupling strength for each gluon mediator 8 in total is identical. Now I'm going to skip a bit in order to mediate the color gauges between quarks you require three Operators \(I_\pm\), \(U_{\pm}\),\( V_{\pm}\) these are the ladder operators for quark color charge interchange. \[(i\gamma_\mu \partial^\mu-m)\Psi=\frac{g_s}{2}\gamma_\mu G^\mu_j(x)\psi\lambda_j\chi_c\] this describes a state \(\chi_c\) with color Couples with the field strength \(g_s\) and changes to another color charge C mediated by \(\lambda_j G_j^G\mu\) I won't go into the fuller color operator expression for each color exchange however the amplitudes for color are not 1/2e as per EM charge color charges are 2/3e or 1/3e so the formulas used for ZPE for those amplitudes are different in wavefunction equivalence due to distinctive difference of the 1/2 EM charges involved for the relevant Meissner effect charges for Em=\(1/2_\pm\) charges for color \(2/3_\pm, 1/3_\pm\) The above qualitatively shows that the field mediation for color charge is significantly distinctive from those of the EM field. This demonstrates that the Meissner effect as per BCS theory or the Anderson-Higgs field do not describe a superconducting QCD vacuum state. for 3 reasons. 1) abelion fields vs non abelion fields. 2) color vs EM charge 3) different coupling strength relations across the mediator fields (EM =different coupling strengths for each mediator as opposed to one coupling strengths for all mediator bosons under QCD 4) the interaction field (mediation requires 2 wavefunctions thereby making it a complex field=added degrees of freedom= higher field number) 5)as this would require significantly more the math I won't delve into it the VeV calculations would be different from a QED VeV from a QCD VeV. Everyone might also note the the above article is looking at 6 Cooper pairs for for QCD vacuum its one of the possibilities. another being Dual Miessner

P is momentum the equation Swansont posted is called the energy momentum relation. https://en.m.wikipedia.org/wiki/Energy–momentum_relation

And that's the trick, we can only garnish indirect evidence. We cannot measure anything less than a quanta of action See here for other readers how that connects to Planck constant and ZPE. https://en.m.wikipedia.org/wiki/Action_(physics)#:~:text=Planck's quantum of action,-The Planck constant&text=%2C is called the quantum of,and the de Broglie wavelength. Now the planck length is the smallest theoretical measurable wavelength. How many planck lengths in the Observsble universe ? Give anyone and idea of the momentum space trend to infinite energy? Using the formulas above for ZPE ?

Ok were going to have to teach you latex above is difficult to read. Anyways take a particle under QFT all particles are field excitations. In terms of ZPE the more you determine localize the position via Compton/De-Debroglie wavelengths the more uncertain you are on its momentum. Yes however a Hermitean matrix the orthogonal diagonal elements have a real number for entry. We're using complex conjugate typically so it's complex conjugate of position and momentum under QM for example. Author doesn't give the relevant details to address that question.

Now take my last post apply that to the quoted section. Little lesson on how to recognize a hermitean matrix.

\[\rho_\Lambda c^2=\int^\infty_0=\frac{4\pi k^2 dk}{(3\pi\hbar)^3}(\frac{1}{2}\sqrt{k^2c^2+m^2c^4})\] The above is a sum over plane waves it doesn't include transverse waves so it's constrained to plane waves only. It also is just first order terms. The reason being for that is the specific action of a harmonic oscillator. Linear only with no non linear components in the above. Now if the above shows the catastrophe is linear read the wiki link under QCD as a complex system will comprise of non linear components. (The tensor fields under SU(3) as one example ) which includes longitudinal and transverse components where the above is longitudinal. If you study the oscillator equations that gives rise to the 1/2 term just prior to the energy momentum under the square root. (Hint U(1) symmetry only in above) do not confuse that as EM only. EM field also has non linear terms

Hmm no actually there is one such theory already but no evidence support some physicists do work on it. So the idea is already being examined though not quite in the way you imagine. (Yes alot of this discussion is applicable to this theory) Boltzmann brains. http://arxiv.org/pdf/1812.01909

notice the integral from summing over momentum states ranges to infinite but the term includes a constraint to prevent that RHS of the \(\int^\infty_0\) that was the regularization term that led to vacuum catastrophe Posted on page 1 That is what needs solving so how does SU(3) solve that ? LMAO I lost count the number of times I stated ENERGY DENSITY this thread.... so earlier I also showed the math showing there are 16 fields which means 16 fields each with a ZPE for QCD as SU(3) for simplicity. Just an FYI to everyone reading for the harmonic oscillator the Operators are Hermitian so it will be equal to its adjoint as all Hermitian operators are. Just in case anyone familiar with Hamilton forms are reading. May also help with sections in regards to the wiki link above (operators being the Hermitian position and momentum operators). What this means is the harmonic operator raising lowering (ladder operators) aka creation/ annihilation operators are also Hermitian

let me ask a different question which people have looked at what zero point energy entails ? Ie which field does it apply to ? All quantum fields have a ZPE ground state this includes all quantum field at the closest QM/QFT allows to absolute zero. Doesnt matter if they are massless or massive or complex mixtures. Every quantum field has a ground state. So what difference would it make to leave the Complex SU(3) field untouched via symmetry breaking if every other field still contributes to the total energy or rather all quantum particle fields draws from the infinite quantum ground state under QFT treatment( where the position and momentum operators are treated at every coordinate for the oscillator field) specifically any quantum field that has not been normalized via the reduced Hamilton ? You could have every single quantum field at absolute zero or any other temperature and still have a ground state The uncertainty principle states that no object can ever have precise values of position and velocity simultaneously. The total energy of a quantum mechanical object (potential and kinetic) is described by its Hamiltonian which also describes the system as a harmonic oscillator, or wave function, that fluctuates between various energy states (see wave-particle duality). All quantum mechanical systems undergo fluctuations even in their ground state, a consequence of their wave-like nature. The uncertainty principle requires every quantum mechanical system to have a fluctuating zero-point energy greater than the minimum of its classical potential well. This results in motion even at absolute zero. For example, liquid helium does not freeze under atmospheric pressure regardless of temperature due to its zero-point energy. https://en.wikipedia.org/wiki/Zero-point_energy so Just how precisely is SU(3) going to solve the vacuum catastrophe if every other quantum field still contributes ? Symmetry breaking or not..... look at graph showing the ground constant at all temperatures... perhaps that will help you understand precisely why I kept mentioning Bose-Einstein and Fermi-Dirac statistics for particle number density ALL fields contribute and ALL fields draw from it for particle creation/annihilation at all temperatures. All quantum fields have harmonic oscillations regardless of temperature. Yet the author claims to somehow magically solve this by leaving SU(3) unbroken in symmetry Thats why I mentioned these equations back on page 5 please read the article in that link.. it will reinforce everything I just described. After you do that , think back on the video MigL posted. then relook at the following from page 1 "lets detail the cosmological constant problem then you can show me how your paper solves this problem I will keep it simple for other readers by not using the Langrene for the time being and simply give a more algebraic treatment. ( mainly to help our other members). To start under QFT the normal modes of a field is a set of harmonic oscillators I will simply apply this as a bosons for simple representation as energy never exists on its own \[E_b=\sum_i(\frac{1}{2}+n_i)\hbar\omega_i\] where n_i is the individual modes n_i=(1,2,3,4.......) we can identify this with vacuum energy as \[E_\Lambda=\frac{1}{2}\hbar\omega_i\] the energy of a particle k with momentum is \[k=\sqrt{k^2c^2+m^2c^4}\] from this we can calculate the sum by integrating over the momentum states to obtain the vacuum energy density. \[\rho_\Lambda c^2=\int^\infty_0=\frac{4\pi k^2 dk}{(3\pi\hbar)^3}(\frac{1}{2}\sqrt{k^2c^2+m^2c^4})\] where \(4\pi k^2 dk\) is the momentum phase space volume factor. the effective cutoff can be given at the Planck momentum \[k_{PL}=\sqrt{\frac{\hbar c^3}{G_N}}\simeq 10^{19}GeV/c\] gives \[\rho \simeq \frac{K_{PL}}{16 \pi^2\hbar^3 c}\simeq\frac{10^74 Gev^4}{c^2(\hbar c)^3} \simeq 2*10^{91} g/cm^3\] compared to the measured Lambda term via the critical density formula \[2+10^{-29} g/cm^3\] method above given under Relativity, Gravitation and Cosmology by Ta-Pei Cheng page 281 appendix A.14 (Oxford Master series in Particle physics, Astrophysics and Cosmology)

your welcome and yes it was me as its a good collection of lectures

everything in that math is what the Author ignored when he states SU(3) all those equations are for quark mass terms. the Higgs mixing angles are included for symmetry breaking this is what the author expects you guys to piece together. So its VERY relevant to the discussion Nothing there will give mass to photons...

That above is nothing more than a representation You do not do any calculations from it. That takes further details. There is nearly 30 different tensors hidden under that expression. You need to factor out the relevant terms in order to apply them. lets demonstrate all of this is contained under that above expression and that is ONLY A TINY PORTION. SU(2) \[{\small\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline Field & \ell_L& \ell_R &v_L&U_L&d_L&U_R &D_R&\phi^+&\phi^0\\\hline T_3&- \frac{1}{2}&0&\frac{1}{2}&\frac{1}{2}&-\frac{1}{2}&0&0&\frac{1}{2}&-\frac{1}{2} \\\hline Y&-\frac{1}{2}&-1&-\frac{1}{2}&\frac{1}{6}&\frac{1}{6}& \frac{2}{3}&-\frac{1}{3}&\frac{1}{2}&\frac{1}{2}\\\hline Q&-1&-1&0&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&-\frac{1}{3}&1&0\\\hline\end{array}}\] \(\psi_L\) doublet \[D_\mu\psi_L=[\partial_\mu-i\frac{g}{\sqrt{2}}(\tau^+W_\mu^+\tau^-W_\mu^-)-i\frac{g}{2}\tau^3W^3_\mu+i\acute{g}YB_\mu]\psi_L=\]\[\partial_\mu-i\frac{g}{\sqrt{2}}(\tau^+W_\mu^-)+ieQA_\mu-i\frac{g}{cos\theta_W}(\frac{t_3}{2}-Qsin^2\theta_W)Z_\mu]\psi_L\] \(\psi_R\) singlet \[D_\mu\psi_R=[\partial\mu+i\acute{g}YB_\mu]\psi_R=\partial_\mu+ieQA_\mu+i\frac{g}{cos\theta_W}Qsin^2\theta_WZ_\mu]\psi_W\] with \[\tau\pm=i\frac{\tau_1\pm\tau_2}{2}\] and charge operator defined as \[Q=\begin{pmatrix}\frac{1}{2}+Y&0\\0&-\frac{1}{2}+Y\end{pmatrix}\] \[e=g.sin\theta_W=g.cos\theta_W\] \[W_\mu\pm=\frac{W^1_\mu\pm iW_\mu^2}{\sqrt{2}}\] \[V_{ckm}=V^\dagger_{\mu L} V_{dL}\] The gauge group of electroweak interactions is \[SU(2)_L\otimes U(1)_Y\] where left handed quarks are in doublets of \[ SU(2)_L\] while right handed quarks are in singlets the electroweak interaction is given by the Langrangian \[\mathcal{L}=-\frac{1}{4}W^a_{\mu\nu}W^{\mu\nu}_a-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}+\overline{\Psi}i\gamma_\mu D^\mu \Psi\] where \[W^{1,2,3},B_\mu\] are the four spin 1 boson fields associated to the generators of the gauge transformation \[\Psi\] The 3 generators of the \[SU(2)_L\] transformation are the three isospin operator components \[t^a=\frac{1}{2} \tau^a \] with \[\tau^a \] being the Pauli matrix and the generator of \[U(1)_\gamma\] being the weak hypercharge operator. The weak isospin "I" and hyper charge \[\gamma\] are related to the electric charge Q and given as \[Q+I^3+\frac{\gamma}{2}\] with quarks and lepton fields organized in left-handed doublets and right-handed singlets: the covariant derivative is given as \[D^\mu=\partial_\mu+igW_\mu\frac{\tau}{2}-\frac{i\acute{g}}{2}B_\mu\] \[\begin{pmatrix}V_\ell\\\ell\end{pmatrix}_L,\ell_R,\begin{pmatrix}u\\d\end{pmatrix}_,u_R,d_R\] The mass eugenstates given by the Weinberg angles are \[W\pm_\mu=\sqrt{\frac{1}{2}}(W^1_\mu\mp i W_\mu^2)\] with the photon and Z boson given as \[A_\mu=B\mu cos\theta_W+W^3_\mu sin\theta_W\] \[Z_\mu=B\mu sin\theta_W+W^3_\mu cos\theta_W\] the mass mixings are given by the CKM matrix below \[\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}\] mass euqenstates given by \(A_\mu\) an \(Z_\mu\) \[W^3_\mu=Z_\mu cos\theta_W+A_\mu sin\theta_W\] \[B_\mu= Z_\mu sin\theta_W+A_\mu cos\theta_W\] \[Z_\mu=W^3_\mu cos\theta_W+B_\mu sin\theta_W\] \[A_\mu=-W^3_\mu\sin\theta_W+B_\mu cos\theta_W\] ghost field given by \[\acute{\psi}=e^{iY\alpha_Y}\psi\] \[\acute{B}_\mu=B_\mu-\frac{1}{\acute{g}}\partial_\mu\alpha Y\] [latex]D_\mu[/latex] minimally coupled gauge covariant derivative. h Higg's bosonic field [latex] \chi[/latex] is the Goldstone boson (not shown above) Goldstone no longer applies after spontaneous symmetry breaking [latex]\overline{\psi}[/latex] is the adjoint spinor [latex]\mathcal{L}_h=|D\mu|^2-\lambda(|h|^2-\frac{v^2}{2})^2[/latex] [latex]D_\mu=\partial_\mu-ie A_\mu[/latex] where [latex] A_\mu[/latex] is the electromagnetic four potential QCD gauge covariant derivative [latex] D_\mu=\partial_\mu \pm ig_s t_a \mathcal{A}^a_\mu[/latex] matrix A represents each scalar gluon field Single Dirac Field [latex]\mathcal{L}=\overline{\psi}I\gamma^\mu\partial_\mu-m)\psi[/latex] under U(1) EM fermion field equates to [latex]\psi\rightarrow\acute{\psi}=e^{I\alpha(x)Q}\psi[/latex] due to invariance requirement of the Langrene above and with the last equation leads to the gauge field [latex]A_\mu[/latex] [latex] \partial_\mu[/latex] is replaced by the covariant derivitave [latex]\partial_\mu\rightarrow D_\mu=\partial_\mu+ieQA_\mu[/latex] where [latex]A_\mu[/latex] transforms as [latex]A_\mu+\frac{1}{e}\partial_\mu\alpha[/latex] Single Gauge field U(1) [latex]\mathcal{L}=\frac{1}{4}F_{\mu\nu}F^{\mu\nu}[/latex] [latex]F_{\mu\nu}=\partial_\nu A_\mu-\partial_\mu A_\nu[/latex] add mass which violates local gauge invariance above [latex]\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\frac{1}{2}m^2A_\mu A^\mu[/latex] guage invariance demands photon be massless to repair gauge invariance add a single complex scalar field [latex]\phi=\frac{1}{\sqrt{2}}(\phi_1+i\phi_2[/latex] Langrene becomes [latex] \mathcal{L}=\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+|D_\mu \phi|^2-V_\phi[/latex] where [latex]D_\mu=\partial_\mu-ieA_\mu[/latex] [latex]V_\phi=\mu^2|\phi^2|+\lambda(|\phi^2|)^2[/latex] [latex]\overline{\psi}=\psi^\dagger \gamma^0[/latex] where [latex]\psi^\dagger[/latex] is the hermitean adjoint and [latex]\gamma^0 [/latex] is the timelike gamma matrix the four contravariant matrix are as follows [latex]\gamma^0=\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}[/latex] [latex]\gamma^1=\begin{pmatrix}0&0&0&1\\0&0&1&0\\0&0&-1&0\\-1&0&0&0\end{pmatrix}[/latex] [latex]\gamma^2=\begin{pmatrix}0&0&0&-i\\0&0&i&0\\0&i&0&0\\-i&0&0&0\end{pmatrix}[/latex] [latex]\gamma^3=\begin{pmatrix}0&0&1&0\\0&0&0&-1\\-1&0&0&0\\0&1&0&0\end{pmatrix}[/latex] where [latex] \gamma^0[/latex] is timelike rest are spacelike V denotes the CKM matrix usage [latex]\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}[/latex] [latex]V_{ckm}=V^\dagger_{\mu L} V_{dL}[/latex] the CKM mixing angles correlates the cross section between the mass eigenstates and the weak interaction eigenstates. Involves CP violations and chirality relations. Dirac 4 component spinor fields [latex]\gamma^5=i\gamma_0,\gamma_1,\gamma_2,\gamma_3[/latex] 4 component Minkowskii with above 4 component Dirac Spinor and 4 component Dirac gamma matrixes are defined as [latex] {\gamma^\mu\gamma^\nu}=2g^{\mu\nu}\mathbb{I}[/latex] where [latex]\mathbb{I}[/latex] is the identity matrix. (required under MSSM electroweak symmetry break} in Chiral basis [latex]\gamma^5[/latex] is diagonal in [latex]2\otimes 2[/latex] the gamma matrixes are [latex]\begin{pmatrix}0&\sigma^\mu_{\alpha\beta}\\\overline{\sigma^{\mu\dot{\alpha}\beta}}&0\end{pmatrix}[/latex] [latex]\gamma^5=i{\gamma_0,\gamma_1,\gamma_2,\gamma_3}=\begin{pmatrix}-\delta_\alpha^\beta&0\\0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] [latex]\mathbb{I}=\begin{pmatrix}\delta_\alpha^\beta&0\\0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] Lorentz group identifiers in [latex](\frac{1}{2},0)\otimes(0,\frac{1}{2})[/latex] [latex]\sigma\frac{I}{4}=(\gamma^\mu\gamma^\nu)=\begin{pmatrix}\sigma^{\mu\nu\beta}_{\alpha}&0\\0&-\sigma^{\mu\nu\dot{\alpha}}_{\dot{\beta}}\end{pmatrix}[/latex] [latex]\sigma^{\mu\nu}[/latex] duality satisfies [latex]\gamma_5\sigma^{\mu\nu}=\frac{1}{2}I\epsilon^{\mu\nu\rho\tau}\sigma_{\rho\tau}[/latex] a 4 component Spinor Dirac field is made up of two mass degenerate Dirac spinor fields U(1) helicity [latex](\chi_\alpha(x)),(\eta_\beta(x))[/latex] [latex]\psi(x)=\begin{pmatrix}\chi^{\alpha\beta}(x)\\ \eta^{\dagger \dot{\alpha}}(x)\end{pmatrix}[/latex] the [latex](\alpha\beta)=(\frac{1}{2},0)[/latex] while the [latex](\dot{\alpha}\dot{\beta})=(0,\frac{1}{2})[/latex] this section relates the SO(4) double cover of the SU(2) gauge requiring the chiral projection operator next. chiral projections operator [latex]P_L=\frac{1}{2}(\mathbb{I}-\gamma_5=\begin{pmatrix}\delta_\alpha^\beta&0\\0&0\end{pmatrix}[/latex] [latex]P_R=\frac{1}{2}(\mathbb{I}+\gamma_5=\begin{pmatrix}0&0\\ 0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] Weyl spinors [latex]\psi_L(x)=P_L\psi(x)=\begin{pmatrix}\chi_\alpha(x)\\0\end{pmatrix}[/latex] [latex]\psi_R(x)=P_R\psi(x)=\begin{pmatrix}0\\ \eta^{\dagger\dot{a}}(x)\end{pmatrix}[/latex] also requires Yukawa couplings...SU(2) matrixes given by [latex]diag(Y_{u1},Y_{u2},Y_{u3})=diag(Y_u,Y_c,Y_t)=diag(L^t_u,\mathbb{Y}_u,R_u)[/latex] [latex]diag(Y_{d1},Y_{d2},Y_{d3})=diag(Y_d,Y_s,Y_b)=diag(L^t_d,\mathbb{Y}_d,R_d[/latex] [latex]diag(Y_{\ell 1},Y_{\ell 2},Y_{\ell3})=diag(Y_e,Y_\mu,Y_\tau)=diag(L^T_\ell,\mathbb{Y}_\ell,R_\ell)[/latex] the fermion masses [latex]Y_{ui}=m_{ui}/V_u[/latex] [latex]Y_{di}=m_{di}/V_d[/latex] [latex]Y_{\ell i}=m_{\ell i}/V_\ell[/latex] Reminder notes: Dirac is massive 1/2 fermions, Weyl the massless. Majorona fermion has its own antiparticle pair while Dirac and Weyl do not. The RH neutrino would be more massive than the LH neutrino, same for the corresponding LH antineutrino and RH Neutrino via seesaw mechanism which is used with the seesaw mechanism under MSM. Under MSSM with different Higgs/higglets can be numerous seesaws. The Majorona method has conservation violations also these fermions must be electric charge neutral. (must be antiparticles of themselves) the CKM and PMNS are different mixing angels in distinction from on another. However they operate much the same way. CKM is more commonly used as its better tested to higher precision levels atm. Quark family is Dirac fermions due to electric charge cannot be its own antiparticle. Same applies to the charged lepton family. Neutrinos are members of the charge neutral lepton family Lorentz group Lorentz transformations list spherical coordinates (rotation along the z axis through an angle ) \[\theta\] \[(x^0,x^1,x^2,x^3)=(ct,r,\theta\phi)\] \[(x_0,x_1,x_2,x_3)=(-ct,r,r^2,\theta,[r^2\sin^2\theta]\phi)\] \[\acute{x}=x\cos\theta+y\sin\theta,,,\acute{y}=-x\sin\theta+y \cos\theta\] \[\Lambda^\mu_\nu=\begin{pmatrix}1&0&0&0\\0&\cos\theta&\sin\theta&0\\0&\sin\theta&\cos\theta&0\\0&0&0&1\end{pmatrix}\] generator along z axis \[k_z=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}\] generator of boost along x axis:: \[k_x=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}=-i\begin{pmatrix}0&1&0&0\\1&0&0&0\\0&0&0&0\\0&0&0&0 \end{pmatrix}\] boost along y axis\ \[k_y=-i\begin{pmatrix}0&0&1&0\\0&0&0&0\\1&0&0&0\\0&0&0&0 \end{pmatrix}\] generator of boost along z direction \[k_z=-i\begin{pmatrix}0&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&0 \end{pmatrix}\] the above is the generator of boosts below is the generator of rotations. \[J_z=\frac{1\partial\Lambda}{i\partial\theta}|_{\theta=0}\] \[J_x=-i\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&1\\0&0&-1&0 \end{pmatrix}\] \[J_y=-i\begin{pmatrix}0&0&0&0\\0&0&0&-1\\0&0&1&0\\0&0&0&0 \end{pmatrix}\] \[J_z=-i\begin{pmatrix}0&0&0&0\\0&0&1&0\\0&-1&0&0\\0&0&0&0 \end{pmatrix}\] there is the boosts and rotations we will need and they obey commutations \[[A,B]=AB-BA\] SO(3) Rotations list set x,y,z rotation as \[\varphi,\Phi\phi\] \[R_x(\varphi)=\begin{pmatrix}1&0&0\\0&\cos\varphi&\sin\varphi\\o&-sin\varphi&cos\varphi \end{pmatrix}\] \[R_y(\phi)=\begin{pmatrix}cos\Phi&0&\sin\Phi\\0&1&0\\-sin\Phi&0&cos\Phi\end{pmatrix}\] \[R_z(\phi)=\begin{pmatrix}cos\theta&sin\theta&0\\-sin\theta&\cos\theta&o\\o&0&1 \end{pmatrix}\] Generators for each non commutative group. \[J_x=-i\frac{dR_x}{d\varphi}|_{\varphi=0}=\begin{pmatrix}0&0&0\\0&0&-i\\o&i&0\end{pmatrix}\] \[J_y=-i\frac{dR_y}{d\Phi}|_{\Phi=0}=\begin{pmatrix}0&0&-i\\0&0&0\\i&i&0\end{pmatrix}\] \[J_z=-i\frac{dR_z}{d\phi}|_{\phi=0}=\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] with angular momentum operator \[{J_i,J_J}=i\epsilon_{ijk}J_k\] with Levi-Civita \[\varepsilon_{123}=\varepsilon_{312}=\varepsilon_{231}=+1\] \[\varepsilon_{123}=\varepsilon_{321}=\varepsilon_{213}=-1\] SU(3) generators Gell Mann matrix's \[\lambda_1=\begin{pmatrix}0&-1&0\\1&0&0\\0&0&0\end{pmatrix}\] \[\lambda_2=\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] \[\lambda_3=\begin{pmatrix}1&0&0\\0&-1&0\\0&0&0\end{pmatrix}\] \[\lambda_4=\begin{pmatrix}0&0&1\\0&0&0\\1&0&0\end{pmatrix}\] \[\lambda_5=\begin{pmatrix}0&0&-i\\0&0&0\\i&0&0\end{pmatrix}\] \[\lambda_6=\begin{pmatrix}0&0&0\\0&0&1\\0&1&0\end{pmatrix}\] \[\lambda_7=\begin{pmatrix}0&0&0\\0&0&-i\\0&i&0\end{pmatrix}\] \[\lambda_8=\frac{1}{\sqrt{3}}\begin{pmatrix}1&0&0\\0&1&0\\0&0&-2\end{pmatrix}\] commutation relations \[[\lambda_i\lambda_j]=2i\sum^8_{k=1}f_{ijk}\lambda_k\] with algebraic structure \[f_{123}=1,f_{147}=f_{165}=f_{246}=f_{246}=f_{257}=f_{345}=f_{376}=\frac{1}{2},f_{458}=f_{678}=\frac{3}{2}\] with Casimer Operator \[\vec{J}^2=J_x^2+J_y^2+j_z^2\] All of that is nothing more than than the relevant details for determining quark mass terms via the CKMS mass mixing matrix

Great, how does that help when the author doesn't show how he determined his conclusions ? I really don't understand why you don't grasp the author made no calculations. \[\mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}\] this solves the cosmological constant problem do you believe me ?

Let me ask you a question. IF i handed you the entire Langrangian for the entire standard model and merely made claims from that Langrangian of say Oh this solves the cosmological constant problem without showing you how to extract the relevant variables and showing how it does so. Would you believe me ? The Standard model Langrangian is rigidly tested so its quite capable of doing so. However why would you believe me if I don't show precisely how it does so? This is the situation with the paper. It's no different Anyone can copy equations and throw them in an article with references. If your not showing precisely how your applying those equations it does absolutely no good. Cross posted with Swansont.

One other possibility as a reference for the image isnt provided it could also indicate the action due to path of least resistance via Euler-Langrangian with the straightline arrow indicating the mean average. I sometimes encounter similar diagrams in least action articles involving gravity. Typically used when describing infinitisimal variations as opposed to more classical treatments. However that's just a possibility without a reference to go by.

So you don't find it distracting trying to add theories not in the original paper to begin with ? The entire discussion of the holographic principle was a literal distraction as it's not in the OP paper. The OP paper had nothing more complex than a little QFT and QED that where it should have stayed. However everyone tried injecting other possibilities through other referenced articles. Forcing everyone to guess and make random assertions.

Perhaps you should reread the original comment. He mentioned other situations he has seen. He never suggested it was involved in this thread.

Langrange polynomial interpolation programming steps for Vandermonde https://people.clas.ufl.edu/kees/files/LagrangePolynomials.pdf

https://inis.iaea.org/collection/NCLCollectionStore/_Public/25/026/25026515.pdf \[d_L\rightarrow U^d_L d_L\] \[d_R\rightarrow U_R^d d_R\] \[u_L\rightarrow U_L^uu_L\] \[u_R\rightarrow U_R^uu_R\] \[\mathcal{L}=\frac{q_2}{\sqrt{2}}[W^+_\mu\bar{u}^i_L\gamma^\mu(V)^{ij}d^j_L+W^-_\mu\bar{d}^i_L\gamma^\mu(V^\dagger)^{ij}\mu^j_L\] \[v_{ckm}=\begin{pmatrix}1&0&0\\0&c_{23}&s_{23}\\0&-s_{23}&c_{23}\end{pmatrix}\begin{pmatrix}c_{13}&0&s_{13}^{1\delta}\\0&1&0\\-s_{13}^{i\delta}&0&c_{13}\end{pmatrix}\begin{pmatrix}c_{12}&s_{12}&0\\-s_{12}c_{12}&0\\0&0&1\end{pmatrix}\] \[\begin{pmatrix}c_{12}c_{13}&c_{12}c_{13}&s_{13}^{-i\delta}\\-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\delta}&c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\delta}&s_{23}c_{13}\\s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\delta}&-c_{12}s_{23}-s_{12}c_{23}-s_{12}c_{23}s_{12}e^{i\delta}&c_{23}c_{12}\end{pmatrix}\] \[s_{ij}=sin\theta_{ij}\] \[c_{ij}=cos\theta_{ij}\] \[ic=[Y_\mu y^\dagger_\mu ,Y_d Y^\dagger_d]=[U_\mu M^\dagger_\mu,U_d M^2_d U^\dagger_d]=U_\mu[M^2_\mu,VM^2_dV^\dagger]U^\dagger_\mu\] Vandermond formula needed for above for next step... Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Nonconservation C.Jarlskog https://kernel-cdn.niconi.org/2021-10-19/1634657105-497108-physrevlett551039.pdf https://pages.cs.wisc.edu/~sifakis/courses/cs412-s13/lecture_notes/CS412_12_Feb_2013.pdf Valndermonde polynomial interpolation for Langrange to reduce computations for curve fitting. https://orionquest.github.io/Numacom/lectures/interpolation.pdf

Try gauge gravity duality Specifically for SU(N) N = 4 Super Yang–Mills theory and type IIB string theory on AdS5 × S5, are identical and therefore describe the same physics from two very different perspectives. In particular, if the AdS/CFT conjecture holds, all the physics of one description is mapped onto all the physics of the other. That's what the conformal element of ads/cft is describing. So now I ask which article does Ashmed specifically apply this under a mathematical treatment without resorting to someone else's work ? Anyone care to take a stab at that ? What I am trying to do is give you a far better understanding of the holographic principle but that requires significant self study to grasp One cannot do that via a forum alone. Ok simple case Take any arbitrary system A and conform it to another system B both systems have a defined boundary so you must have some translation between system A and system B The conformal element... So take an SU(N) system and conform it to a Maximally symmetric anti-Desitter spacetime there are only 3 Maximally symmetric spacetimes known De-Sitter/anti-Desitter and Minkowskii. That is the Principle basis of the holographic principle and how its applied to quantum fields. So have you ever studied string theory which would be required ? Have you studied how some point like particle property can be mapped through a mathematical space via a function which is true in string theory ? what are the boundaries of a closed string vs an open string ? how is charge mapped for start and end points in string theory ? how can one understand how the holographic principle works in ADS/CFT if they can't answer those questions ? You have to study from the start of how the theory is developed rather than jumping to the end.... The most important part the physics of system A must be identical to the physics of system B In order to be conformed... If you want to understand String theory I suggest String theory Demystified by David McMahon its about the easiest textbook on String Theory I have encountered How am I confident the OP paper doesn't involve the holographic principle ? its simple the Langrangian forms he provided do not include any terms for SUSY. In essence the entire discussion on the holographic principle has been nothing more than trying to fit personal favorite theories into someone else's model. I recommend you don't rely on pop media coverage every theory always has competing theories that's all part of the scientific method. Those findings are not conclusive they merely hint at the possibility.

Clue given by Joigus (gauge gravity duality now try and find the duality for SU(3). Requirement above but also must produce Cooper pairs for Meissner effect. There is a particular key theory I want to see if the defenders can identify.

Your welcome a personal sidenote it was that very detail that got my dissertation on quintessence inflation to get invalidated wrong equation of state to observational evidence. It was written prior to WMAP using COBE dataset. A side note @MJ kihara the illusion statement you gave earlier was a Berkenstein descriptive so I cannot fault you on that. You cannot be faulted for something contained in peer review literature.

Slight correction it depends on how the vacuum is defined. If it's a vacuum with an equation of state other than w=-1 such as a quintessence vacuum it would dilute any vacuum with equation of state w=-1 such as the cosmological term does not. The rest of the above I agree with

My favorite is Penquinn diagrams for certain Feymann integrals.