Artifact f319f49f7a0f83102985af16222968270b54c59bf76e026634936a87ceb9466b:
- Executable file
r37/packages/assist/selfgra.tst
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 7313) [annotate] [blame] [check-ins using] [more...]
- Executable file
r38/packages/assist/selfgra.tst
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 7313) [annotate] [blame] [check-ins using]
%%%%%%%%%%%%%%%%%%% A. Burnel and H. Caprasse %%%%%%%%%%%%%%%%%%%%%% % % Application of CANTENS.RED % Date: 15/09/98 % % Computes the gluon contribution to the gluon self-energy in the % "finite" theory % contains initially 18 terms which are reduced to 10 by cantens % in a dm-dimensional Minkowski space and 8 terms in a 4-dimensional % Minkowski space. % % *** Will look much nicer if run in the GRAPHIC mode % % LOADING CANTENS load cantens$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Structure definitions, Minkowski space X internal symmetry space %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% off onespace; % to be allowed to work within several subspaces define_spaces wholespace={dm+di,signature=1}; define_spaces mink={dm,signature=1};%,indexrange=0 .. 3}; define_spaces internal={di,signature=0};%,indexrange=4 .. 11}; % % Memberships of indices: mk_ids_belong_space({mu1,mu2,nu1,nu2,tau},mink); mk_ids_belong_space({a1,a2,b1,b2,c1,c2},internal); %%%%%%%%%%%%%%%% % Used Tensors % %%%%%%%%%%%%%%%% %% variables x1,x2 and xi=x1-x2, %% aa, gluon field %% dd, contracted gluon field %% which appears inside the expression %% a is the antisymmetric structure constant of SU3. %% It is called "a" to assure that it appears first %% inside REDUCE expressions and to assure that they %% factorize in front of the output expression. % tensor aa,dd,a,x1,x2,xi; % tensor declaration make_variables x1,x2,xi; % variable declaration % declare to which subspace the declared tensors belong to. make_tensor_belong_space(x1,mink); make_tensor_belong_space(x2,mink); make_tensor_belong_space(xi,mink); make_tensor_belong_space(a,internal); antisymmetric a; % antisymmetry of structure constant. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % building of starting expression to be manipulated and simplified. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% es1:=g^2*a(a1,b1,c1)*a(a2,b2,c2); as1:=-aa(x1,nu1,-b1)*aa(x2,nu2,-b2)*df(df(dd(xi,mu1,-c1,mu2,-c2),xi(nu1)),xi(nu2)) *dd(xi,-mu1,-a1,-mu2,-a2); as2:=-aa(x1,nu1,-b1)*aa(x2,nu2,-b2)*df(dd(xi,mu1,-c1,mu2,-a2),xi(nu1)) *df(dd(xi,-mu1,-a1,-mu2,-c2),xi(nu2)); as3:=aa(x1,nu1,-b1)*df(aa(x2,mu2,-c2),x2(nu2))*df(dd(xi,mu1,-c1,nu2,-b2),xi(nu1)) *dd(xi,-mu1,-a1,-mu2,-a2); as4:=aa(x1,nu1,-b1)*df(aa(x2,mu2,-c2),x2(nu2))*df(dd(xi,mu1,-c1,-mu2,-a2),xi(nu1)) *dd(xi,-mu1,-a1,nu2,-b2); as5:=-aa(x1,nu1,-b1)*aa(x2,mu2,-a2)*df(dd(xi,mu1,-c1,nu2,-b2),xi(nu1)) *df(dd(xi,-mu1,-a1,-mu2,-c2),xi(nu2)); as6:=-aa(x1,nu1,-b1)*aa(x2,mu2,-a2)*df(df(dd(xi,mu1,-c1,-mu2,-c2),xi(nu1)),xi(nu2)) *dd(xi,-mu1,-a1,nu2,-b2); as7:=-df(aa(x1,mu1,-c1),x1(nu1))*aa(x2,nu2,-b2)*df(dd(xi,nu1,-b1,mu2,-c2),xi(nu2)) *dd(xi,-mu1,-a1,-mu2,-a2); as8:=-df(aa(x1,mu1,-c1),x1(nu1))*aa(x2,nu2,-b2)*df(dd(xi,-mu1,-a1,mu2,-c2),xi(nu2)) *dd(xi,nu1,-b1,-mu2,-a2); as9:=df(aa(x1,mu1,-c1),x1(nu1))*df(aa(x2,mu2,-c2),x2(nu2))*dd(xi,nu1,-b1,nu2,-b2) *dd(xi,-mu1,-a1,-mu2,-a2); as10:=df(aa(x1,mu1,-c1),x1(nu1))*df(aa(x2,mu2,-c2),x2(nu2))*dd(xi,nu1,-b1,-mu2,-a2) *dd(xi,-mu1,-a1,nu2,-b2); as11:=-df(aa(x1,mu1,-c1),x1(nu1))*aa(x2,mu2,-a2)*df(dd(xi,-mu1,-a1,-mu2,-c2),xi(nu2)) *dd(xi,nu1,-b1,nu2,-b2); as12:=-df(aa(x1,mu1,-c1),x1(nu1))*aa(x2,mu2,-a2)*df(dd(xi,nu1,-b1,-mu2,-c2),xi(nu2)) *dd(xi,-mu1,-a1,nu2,-b2); as13:=-aa(x1,mu1,-a1)*aa(x2,nu2,-b2)*df(dd(xi,nu1,-b1,mu2,-c2),xi(nu2)) *df(dd(xi,-mu1,-c1,-mu2,-a2),xi(nu1)); as14:=-aa(x1,mu1,-a1)*aa(x2,nu2,-b2)*dd(xi,nu1,-b1,mu2,-a2) *df(dd(xi,-mu1,-c1,-mu2,-c2),xi(nu1),xi(nu2)); as15:=aa(x1,mu1,-a1)*df(aa(x2,mu2,-c2),x2(nu2))*dd(xi,nu1,-b1,nu2,-b2) *df(dd(xi,-mu1,-c1,-mu2,-a2),xi(nu1)); as16:=aa(x1,mu1,-a1)*df(aa(x2,mu2,-c2),x2(nu2))*dd(xi,nu1,-b1,-mu2,-a2) *df(dd(xi,-mu1,-c1,nu2,-b2),xi(nu1)); as17:=-aa(x1,mu1,-a1)*aa(x2,mu2,-a2)*df(dd(xi,-mu1,-c1,-mu2,-c2),xi(nu1),xi(nu2)) *dd(xi,nu1,-b1,nu2,-b2); as18:=-aa(x1,mu1,-a1)*aa(x2,mu2,-a2)*df(dd(xi,-mu1,-c1,nu2,-b2),xi(nu1)) *df(dd(xi,nu1,-b1,-mu2,-c2),xi(nu2)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % building of the gluon contribution to gluon self-energy % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% es:=es1*for i:=1:18 sum mkid(as,i); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Are some terms identical ? % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% es:=canonical es; length es; % no simplification tensor dc; % new tensor make_tensor_belong_space(dc,mink); % belongs to Minkowski space make_partic_tens(rho,metric); % "rho" is a metric tensor make_tensor_belong_space(rho,internal); % in the internal space %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % rewriting rule and subsequent simplification % % dd(mu1,mu2,a,b)=>rho(a,b)*dc(mu1,mu2) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ddrule:={dd({~xi},~a,~b,~c,~d)=>rho(b,d)*dc({xi},a,c)}; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % simplification after application of the rule % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% es:=(es where ddrule); % es:=canonical es; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Particular gauge: % % case of Fermi gauge : dc(mu1,mu2)=g(mu1,mu2)*dc % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% make_partic_tens(delta,delta); % delta tenseur defined with name "delta" % eta tenseur introduced with name "eta": make_partic_tens(eta,eta); make_tensor_belong_space(eta,mink); % rule for the choice of gauge: dcrule:={dc({~xi},~a,~c)=>eta(a,c)*dc(xi)}; % rewriting of the expression res:=(es where dcrule); % simplification res:=canonical res; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % last rewriting rule: % % second derivative of dc(xi) with % % respect to xi tensor is zero % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dalrule:={df(dc(xi),xi(~a),xi(-~a))=>0}; res:=(res where dalrule); canonical res - res; % gives 0 length res; dm:=4; % particularization to 4-dimensional Minkowski space res4:=res; length res4; % 8 is the correct number of terms. end; %in "skelsplt.red"; tensor ff; %symtree(ff,{!*,{!-,1,2},3}); symbolic procedure nordpl(u,v); if listp u and listp v then nordp(cadr u,cadr v) else if listp u then nordp(cadr u,v) else if listp v then nordp(u,cadr v) else nordp(u,v); flag('(nordpl),'opfn); %frule:={df(aa({x1},~mu1,~b),x1(~mu2))=>ff({x1},-mu2,mu1,b)+df(aa({x1},-mu2,b),x1(-mu1)) % when nordpl(mu1,mu2)}; %ffrule:={df(aa({x2},~mu1,~b),x2(~mu2))=>ff({x2},-mu2,mu1,b)+df(aa({x2},-mu2,b),x2(-mu1)) % when nordpl(mu1,mu2)}; frule:={df(aa({~x1},~mu1,~b),~x1(~mu2))=>ff({x1},-mu2,mu1,b)+df(aa({x1},-mu2,b),x1(-mu1)) when nordpl(mu1,mu2)}; res4 where frule;