Mordred

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.

The simplest article on holographic superconductors I could find is above in that quoted section the Langrangian it gives that will produce the superconducting Cooper pairs is \[\mathcal{L}=R+\frac{6}{L^2}-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-|\nabla_\phi-iq A\phi|^2-m^2|\phi^2\] R is the Ricci scalar \[F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu\] is the Maxwell field strength tensor \(\phi\) being the scalar with charge q and is related by the order parameter \(\langle \phi_b\rangle\) what the article describes is the superconductivity of the dual gravity boundary of the anti-Desitter spacetime and the conformal theory spacetime see Penrose diagrams. The anti-Desitter is constant negative curvature that is what defines the surface element boundary where the holographic superconductor can be applied. So I ask how is the author applying the above to the entire Universe ? I will let the defenders mathematically show how this is possible (ps there is a way and treatments doing so but I want the defenders to supply them ) https://phas.ubc.ca/~berciu/TEACHING/PHYS502/PROJECTS/20-HolSC-SB2.pdf I'm not asking anyone to do their own calculations they may certainly do as I just did supply a reference pointing out the specified equations involved. why are they looking at BH's has to do with the EH and Hawking radiation the Blackbody temperature of an EH is colder than the blackbody temperature of the Universe. via \[T_H=\frac{\hbar c^3}{8\pi GM k_b}\]

It's not an illusion it's a mathematical methodology at dimensional reduction a means that's helpful to eliminate unwanted degrees of freedom to better examine specific processes. It's all the glamour kings that treat it as an illusion the metaphysics wannabe physicists. The ones that pay more attention to verbal descriptions than the mathematics. The same people that think higher dimensions past 4 is some alternative reality unperceived instead of an effective degree of freedom . Take ADS/CFT for example anti Desitter (Maximally symmetric spacetime) under conformal field treatment using string theory. String theory is conformsl doesn't use integrals it uses differential equations for curve fitting. GR is another conformal field theory. QFT is canonical it uses integrals. Both methodologies can describe precisely the same system with equal accuracy. Integrals are more useful for wavefunctions due to Fourier transformations. What ppl think are illusions is mathematical spaces that have zero physicality. Just as momentum space or phase space. Or branes for string theory. Specifically a graph of a given function. Ie a chart and when you multiple charts you need an atlas. Just as you need a transformation between graphs. Every physics treatment method uses the above in one fashion or another.

You can I already stated what one can learn the IR and UV limits of the SU(3) strong force that is the essence of studying the SU(3) gauge to understand its divergences at a wider range of temperatures. We study the high energy limits at particle accelerators we study the opposite range in condendates. My studies is the high end range as my specialty being early universe.

Lets take a simple example how many members are aware that all functions are graphs but not all graphs are functions? How do you test if a graph is a function ? I only know of a few members that would be able to answer that How would anyone understand a symmetry group without knowing how to apply vector algebra? It's impossible you need vector algebra you need to recognize what the components of a vector are. How to use vector algebra on inner outer and cross products of vectors prior to leaning what a one form or dual vector is to understand what a covariant or cobnteavariant vector is. Otherwise tensors will always be mysterious and if you can't understand tensors you won't understand symmetry groups. If someone doesn't have these skills they cannot compete with physicists that do these are prerequisite skills you need just to an undergrad course in physics.

In all honesty and undergrad could do a better job. Many of those equations merely look complicated. The equations in the OP paper are essentially first order terms. You recall that video Migl posted that stuff is taught within the first term of a cosmology related program and can be found in introductory textbooks. It did a better job than the paper. One doesn't calculate integrals, you derive the portions you require using something like the Feymann trick. You don't try to sum amplitudes of an integral you use the Cassimer trick. To ppl that never took variations of calculus of course integrals look nasty. Yet we have tools such as Feycalc through mathematic. In that entire paper not a single formula cannot be found in other references. Not a single equation literally there is zero evidence of the author doing his own math. It's all on the backbone of other ppls work. In point of detail it literally claimed to give mass by slapping in the particle datagroup constraint on photon mass yet claimed that as the photon gaining mass through symmetry breaking and ppl are defending that?? Are they blind or like being lied to I don't know I pointed that out a while ago but obviously some people don't know how to listen. Careful here a Bose-Einstein condensate is something producable in a lab. It's properties are well studied and are being studied. It's not something that our universe naturally produces unless you have environment significantly colder than our universe balckbody temperature. Careful here a Bose-Einstein condensate is something producable in a lab. It's properties are well studied and are being studied. It's not something that our universe naturally produces unless you have environment significantly colder than our universe balckbody temperature. Here is one such lab https://equs.org/aol It's not something that's occurring in outer space today. Our universe balckbody temperature 2.73 Kelvin is too hot. Lets put it this way our universe would have to be in heat death to naturally produce Bose-Einstein condensates throughout the universe on a universe global scale. Yes you can apply the holographic principle to those lab samples but not in the manner ppl tend to think of the holographic principle. \[SU(3)_L\otimes SU(3)_R\mathbb{Z}/2\] in String theory the boundary conditions is the Dirichlet and Neumann boundary conditions same as those in a calculus textbook. That's the boundaries essentially though there are so many variations of lattice network treatments they are often under different names that's why I posted several textbook Style Articles on condensates earlier this thread. Has anyone bothered to read them ? Here they are again... Many someone will read them this go around. Lol if our universe were that cold to produce condensates on a global scale black holes themselves would start evaporating via Hawking radiation. That is a very evident proof that the \[10^{123}\] is easily falsifiable. Want to really learn physics study Calculus and statistical mechanics by the time you get through 2 or 3 textbooks you will understand physics better than 90 percent of our forums members.

Yeah apparently people want to defend something poorly written to begin with. I don't know about anyone else I would be disgusted with myself if I had written that paper regardless of the quality of other references but that's just my opinion. If that paper is an indication of his best work it needs improvement. I've examined undergrad dissertation practice papers of better quality.

Yes but then ask yourself why is there so many confusing statements instead of including the related mathematics within the same paper instead of trying to advertise every paper he has ever written ? For example why wasnt the QCD langrangisn included for SU(3) instead of just putting in the QED langrangian? Why isn't his SU(3) atoms professionally defined in the paper so there is zero chance of confusion ? Attaching the term atom to SU(3) is something I have never seen in any other professionally written paper. SU(3) gauge group absolutely SU(3) atom never before As stated previously within the paper I do not see a single calculation or derivative that is his own What really drives me up the wall is when the author threw in the particle data group constraint for the photon and claimed it was coupled to the Higgs field as acquiring mass but only showing the QED langrangian without any Higgs term

That may very well be true but its not included in the article under discussion. I noted that numerous times on page one. The discussion is the OP paper itself we shouldn't have to piece meal it together through dozens of other literature. His later or earlier articles may very well be excellent but the discussion is the OP paper. I'm not about to go scrounching and searching however many papers the author wrote or didn't write to justify the OP paper.

Snyders spacetime can be applied to the quantum oscillator certainly but it doesn't do anything for number density of particles. Here is the treatment https://arxiv.org/abs/1308.0673 For the harmonic oscillator under Snyder. How familiar are you with the terms Abelion vs non abelion ? In terms of symmetry groups as that is relevant to the opening paragraph of the above article.