2) According to Olaf's "03 posdzech - grafiken berlin 1994.pdf" (in protosimplex website), page 8, R3+T+S is "materielle Welt" and I+G is "nichtmaterieller Hintergrund der Welt", and is "Zeitlos". What does that mean ?

will314159

13th March 2006 - 08:16 PM

In case anybody has had problems downloading, here is the Maxima particle mass code

**********************8

/* Maxima version of Heim Theory Mass Equations by Martin Andrews (mdda123) */

/* Thanks to John Reed for the original Mathematica™ source to work from */

/* BSD : retain credits above */

map(texput,['Alpha,'Alpha_Plus,'Alpha_Minus], ["\\alpha","\\alpha_\plus","\\alpha_\minus"])$

map(texput,['Beta,'Gamma,'Eta,'Theta,'Sigma], ["\\beta","\\gamma","\\eta","\\theta","\\sigma"])$

texput('Epsilon0, "\\epsilon_0")$

texput('hBar, "\\hbar")$

texput('Mu, "\\mu")$

texput('Mu0, "\\mu_0")$

texput('Z0, "Z_0")$

map(texput,['Qn,'Qm,'Qp,'Q_Sigma], ["Q_n","Q_m","Q_p","Q_\sigma"])$

map(texput,['Nk,'NkPrime,'N1,'N2,'N3,'N4,'N5,'N6], ["N_k","N_k^\prime","N_1","N_2","N_3","N_4","N_5","N_6"])$

texput('CapitalPhi, "\\Phi")$

fprec:30;

"numer:true;";

numer:false;

simp:false;

hBar:6.6260693*10^-34/(2*%pi);

c:299792458;

Gamma:6.6732*10^(-11);

Epsilon0:8.8542*10^(-12);

Mu0:4*%pi*10^(-7);

Z0:376.730313461;

kgMev:.56095892*10^30;

Alpha:1/137.03599976;

Beta:.9999859019908;

Eta(q,k):=(%pi/(%pi^4+(4+k)*q^4)^(1/4));

Theta(q,n):=5*Eta(q,n)+2*sqrt(Eta(q,n))+1;

Mu:%pi^(1/4)*(3*%pi*Gamma*hBar)^(1/3)*sqrt(c*hBar/(3*Gamma))/c;

Xi:1.61803398874989;

N1:1/2*(1+sqrt(Eta(q,k)));

N2:(2/3)*1/Eta(q,k);

Alpha_Plus:Eta(1,0)^(1/6)/Eta(1,0)^2*(1-Theta(1,0)*((2*(1-sqrt(Eta(1,0))))/(Eta(1,0)*(1+sqrt(Eta(1,0)))))^2*sqrt(2*Eta(1,0)))-1;

Alpha_Minus:(Alpha_Plus+1)*Eta(1,0)-1;

AA1:(8/Eta(1,0))*(1-Alpha_Minus/Alpha_Plus)*(1-3*Eta(1,0)/4);

s:k^2+1;

Qn:3*2^(s-2);

Qm:2^s-1;

Qp:2^s+2*(-1)^k;

Q_Sigma:2^(s-1)-1;

"Nk, Nk', N1,N2,N3,N4,N5,N6 : Checked vs paper";

Nk :Qn+Qm+Qp+Q_Sigma+k*(-1)^k*2^(k^2-1);

NkPrime:Qn+Qm+Qp+Q_Sigma-2*k-1;

N3:block([uu,co,oc,zw2,zw3a,zw3,zw1,zw5,zw4,zw4a],

uu:2*%pi*%e,

co:3/4,

oc:4/3,

zw2 :1+sqrt(Eta(q,1)),

zw3a:1-sqrt(Eta(1,0)),

zw3:zw3a^2,

zw1:uu^2*co*2*(zw2)/((1-Eta(1,0))*Theta(1,0))-1,

zw5:(k-1)*(1-%pi*(1-Eta(q,k))/zw2)*(1-uu*(Eta(q,1)/Theta(q,1))*(1-Alpha_Minus/Alpha_Plus)*zw3),

zw4:-zw3*zw1*oc/uu,

zw4a:zw5+zw4,

exp(zw4a)*2/k);

N4:(4/k)*(1+q*(k-1));

N5:AA1*(1+k*(k-1)*2^(k^2+3)*Nk*AA1*((1-sqrt(Eta(q,k)))/(1+sqrt(Eta(q,k))))^2);

N6:2*k/(%pi*%e*Theta(1,0))*(sqrt(k)*(k^2-1)*Nk/sqrt(Eta(1,k))*(q-(1-q)*NkPrime/(Qn*sqrt(Eta(1,k))))+(-1)^(k+1))*Eta(1,0)*(1-Alpha_Minus/Alpha_Plus)*(4*(1-sqrt(Eta(1,0)))/(1+sqrt(Eta(1,0))))^2*Q_Sigma;

HH:Qn+Qm+Qp+Q_Sigma;

g :Qn^3+Qm^2+Qp/k*exp(k-1)+exp((1-2*k)/3)-HH*(k-1);

AA:8*g*HH*(2-k+8*HH*(k-1))^(-1);

BB:3*HH/(k^2*(2*k-1));

NN:0;

electron :[name="e-", k=1,n=0, m=0, p=0, Sigma=0, PP=1,QQ=1,Kappa=0,qL=-1,q=1];

nelectron :[name="e0", k=1,n=0, m=0, p=0, Sigma=1, PP=1,QQ=1,Kappa=0,qL=0, q=0];

muon :[name="Mu", k=1,n=11, m=6, p=11,Sigma=6, PP=1,QQ=1,Kappa=1,qL=-1,q=1];

Etapart :[name="Eta", k=1,n=18, m=22,p=17,Sigma=14,PP=0,QQ=0,Kappa=0,qL=0,q=1];

Kplus :[name="K^+", k=1,n=17, m=26, p=30, Sigma=28, PP=1, QQ=0, qL=1, Kappa=1, q=1];

Kzero :[name="K^0", k=1,n=18, m=5, p=5, Sigma=2, PP=1, QQ=0, qL=0, Kappa=1, q=0];

PiPlus :[name = "Pi^+", k=1, n=12, m=9, p=2, Sigma=3, PP=2, QQ=0, qL=1, Kappa=0, q=1];

PiZero :[name = "Pi^0", k=1, n=12, m=3, p=6, Sigma=4, PP=2, QQ=0, qL=0, Kappa=0, q=0];

Lambda :[name="CapitalLambda", k=2, n=1, m=3, p=0, Sigma=-11, PP=0, QQ=1, qL=0, Kappa=0, q=0];

OmegaMinus:[name="CapitalOmega^-", k=2, n=4, m=4, p=-1, Sigma=-15, PP=0, QQ=3, qL=-1, Kappa=0, q=1];

proton :[name="p", k=2,n=0, m=0, p=0, Sigma=0, PP=1, QQ=1, qL=1, Kappa=0, q=1];

neutron :[name="n", k=2,n=0, m=0, p=-2, Sigma=17, PP=1, QQ=1, qL=0, Kappa=0, q=0,Epsilon=0];

XiMinus :[name = "CapitalXi^-", k=2, n=2, m=7, p=-17, Sigma=2, PP=1, QQ=1, qL=-1, Kappa=1, q=1];

XiZero :[name = "CapitalXi^0", k=2, n=2, m=6, p=-1, Sigma=6, PP=1, QQ=1, qL=0, Kappa=1, q=0];

SigmaPlus :[name = "CapitalSigma^+", k=2, n=2, m=-7, p=-12, Sigma=10, PP=2, QQ=1, qL=1, Kappa=0, q=1, Epsilon=1];

SigmaZero :[name = "CapitalSigma^0", k=2, n=2, m=-7, p=-14, Sigma=-2, PP=2, QQ=1, qL=0, Kappa=0, q=0, Epsilon=1];

SigmaMinus:[name = "CapitalSigma^-", k=2, n=2, m=-6, p=-5, Sigma=-8, PP=2, QQ=1, qL=-1,Kappa=0, q=1, Epsilon=1];

quantum:[electron,nelectron,muon,Etapart,Kplus,Kzero,PiPlus,PiZero,Lambda,OmegaMinus,proton,neutron,XiMinus,XiZero,SigmaPlus,SigmaZero];

Leptons:[electron,muon];

Mesons:[PiPlus,PiZero,Etapart,Kplus,Kzero];

Baryons:[proton,neutron,Lambda,SigmaPlus,SigmaMinus,SigmaZero,XiMinus,XiZero,OmegaMinus];

LeptonObserved:[.51099907,105.658389];

MesonObserved :[139.57018,134.9766,547.30,493.677,497.672];

BaryonObserved:[938.2731,939.56563,1115.683,1189.37,1197.449,1192.642,1321.32,1314.9,1672.45];

"# These appear to be superceeded by the (Lex ~= LL), x and Wn0 defined below;";

"# So they become the same, update 1/4BB in x to 1/(4BB);";

"x :(1-QQ-binomial(PP,2))*(2-k)+1/4*BB*(a1+k^3/(4*HH)*(a2+a3/(4*BB)));";

"

LL :(1-Kappa)*QQ*(2-k);

x :(1-QQ-binomial(PP,2))*(2-k)+1/(4*BB)*(a1+k^3/(4*HH)*(a2+a3/(4*BB)));

Wn0:AA*exp(x)*(1-Eta(1,0))^LL+(PP-QQ)*(1-binomial(PP,2))*(1-binomial(QQ,3))*(1-sqrt(Eta(1,0)))^2*sqrt(2);

";

"# a1 checked vs. paper";

a1():=block([z1,z2,z3],

z1:1+BB+k*(QQ^2+1)*binomial(QQ,3)-Kappa*((BB-1)*(2-k)-3*(HH-2*(1+q))*(PP-QQ)+1),

z2:(3*(2-q)*binomial(PP,2)-QQ*(3*(PP+QQ)+q))*(2-k),

z3:(1+(BB/k)*(k+PP-QQ))*(1-binomial(PP,2))*(1-binomial(QQ,3)),

z1-(1-Kappa)*(z2+(k*(PP+1)*binomial(PP,2)+z3-q*(1-q)*binomial(QQ,3))*(k-1)));

"# part4 is from Fortran - differs from Paper B29";

a2():=block([z4,z5,z6,z7,z8,z9,part1,part2,part3,part4],

part1:BB*(1-binomial(QQ,3)*(1-binomial(PP,3)))+6/k-Kappa*(QQ/2*(BB-7*k)-(3*q-1)*(k-1)+1/2*(PP-QQ)*(4+(BB+1)*(1-q))),

z4: PP*(BB/2+2+q),

z5:-QQ*(BB/2+(1-4*(1+4*q))),

part2:(z4+z5)*(2-k),

z6:1/4*(BB-2)*(1+3/2*(PP-QQ)),

z7:-1/2*BB*(1-q),

z8:(1/2*(BB+q-Epsilon*qL)+3*Epsilon*qL)*(2-Epsilon*qL),

z9:-1/4*(BB+2)*(1-q),

part3:(z6+z7-binomial(PP,2)*(z8+z9))*(1-binomial(QQ,3))*(k-1),

part4:-binomial(PP,3)*((2*(1+Epsilon*qL)+1/2*(2-q)*(3*(1-q)+Epsilon*qL)-q)-1/4*q*(1-q)*(BB-4)-1/4*(BB-2)+1/2*B*(1-q)),

part1-(1-Kappa)*(part2+part3+part4)) $

"# checked vs. Mathematica";

a3():=block([wet,zw,z1,z2,z3,z4,z5,zw1,y1,y],

wet:sqrt(Eta(1,0)),

zw:(wet/k)*(4*(2-wet)-%pi*(1-Eta(1,0))*wet)*(k+wet*(k-1))+5*(1-q)*(4*BB+PP+QQ)/(2*k+(-1)^k),

z2:(PP-1)*(PP-2)*(2*(HH+2)/k^2+(2-k)/(2*%pi)),

z3:q*BB/2*(BB+2*(PP-QQ)),

z1:(PP*(PP+2)*BB+(PP+1)^2-q*(1+Epsilon*qL)*(k*(PP^2+1)*(BB+2)+(PP^2+PP+1)/4)-q*(1-Epsilon*qL)*(BB+PP^2+1))*(k-1),

z4:((PP-QQ)*(HH+2)+PP*(5*BB*(1+q)*QQ+k*(k-1)*(k*(PP+QQ)^2*(HH+3*k+1)*(1-q)-(BB+6*k)/2)))*(1-binomial(QQ,3))*(1-binomial(PP,2)),

z5:(Epsilon*qL*(BB+2*QQ+1)+q/2*(1-Epsilon*qL)*(2*k+1)/k+(1-q)*(QQ^2+1+2*BB))*QQ*(2-q)*binomial(PP,3),

zw1:z2+binomial(PP,2)*(1-binomial(QQ,3))*(z3+z1)+z4+z5,

y1:Kappa*zw+(1-Kappa)*zw1,

y:y1/(2*BB),

(4*BB)*y/(1+y)-1/(4+BB)) $

"###This potentially hangs on the x line if simp:true" $

Wn0:block([Lex,x,wsmalln0,zw],

x:(1-QQ-binomial(PP,2))*(2-k) + (a1()+1/4*(k^3/HH)*(a2()+a3()/(4*BB)))/(4*BB),

Lex:(1-Kappa)*QQ*(2-k),

wsmalln0:AA*exp(x)*(1-Eta(1,0))^Lex,

zw:(PP-QQ)*(1-binomial(PP,2)*(1-binomial(QQ,3))),

wsmalln0+zw*(1-sqrt(Eta(1,0)))^2*sqrt(2)) $

CapitalPhi:PP*(PP+QQ)*N5*(-1)^(PP+QQ)+QQ*(PP+1)*N6 $

GG:N1*(Qn*(1+Qn))^2+N2*Qm*(2*Qm^2+3*Qm+1)+N3*Qp*(Qp+1)+4*Q_Sigma $

SS:N1*( n*(1+ n))^2+N2* m*(2* m^2+3* m+1)+N3* p*( p+1)+4* Sigma $

UU:if(NN=0) then (

2^(k+Kappa+PP+QQ)/(Eta(q,k)^2)*(PP^2+3/2*(PP-QQ)+PP*(1-q)+4*Kappa*BB*(1-QQ)/(3-2*q)+(k-1)*(PP+2*QQ-4*%pi*(PP-QQ)*(1-q)/2^(1/4)))

) else 0;

Phi:if(NN=0) then (

N4*p^2/(1+p^2)*(Sigma+Q_Sigma)/sqrt(1+Sigma^2)*(2^(1/4)-4*BB*UU/Wn0)+PP*(PP-2)^2*(1+Kappa*(1-q)/(2*Alpha*Theta(1,0)))*(%pi/%e)^2*sqrt(Eta(1,2))*(Qm-Qn)-(PP+1)*binomial(QQ,3)/Alpha

) else 0;

FF:N1*(2*n*Qn*(1+3*(n+Qn+n*Qn)+2*(n^2+Qn^2)))+N2*(6*m*Qm*(1+m+Qm))+N3*(2*p*Qp)+Phi;

"# Now the mass can be calculated...";

sum1:Mu*(GG+SS+FF+CapitalPhi)*Alpha_Plus $

sum2:4*Mu*q*Alpha_Minus $

Mass:kgMev*(sum1+sum2) $

"ev(Mass,electron),numer;";

"block([r],r:sublis(electron,Mass), ev(r,numer,simp));";

"map(lambda ([aa], subst(aa, L1)), L2); ";

"map(lambda([aa], block([r], r:sublis(aa, Mass), ev([name,r],aa,numer,simp))), [electron, proton]); ";

"M:matrix(map(lambda([aa], block([r], r:sublis(aa, Mass), ev([name,r],aa,numer,simp))), quantum)); ";

SafeCalc(qtys,particle):=block([r], r:sublis(particle, qtys), ev(qtys,particle,numer,simp)) $

"Mass of the Electron:";

SafeCalc(Mass,electron);

"Mass of all the particles:";

M:matrix(map(lambda([aa],SafeCalc([name,Mass],aa)), quantum));