ERGE.nb

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******************\n\n*insert end markers (rotating Tr if required)\nid \
Tr(?a,dtRM(?b),?c)=Tr(?c,?a,dtRM(?b));\nid Tr(?a)=Tr(?a,end);\n\n*remove Tr\n\
Repeat; \nid Tr(nfF?(?a),?b)=nfF(?a)*Tr(?b);\nid Tr(nfF?,?b)=nfF*Tr(?b);\nid \
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******************************************************************************\
**\n* carry out derivatives\nRepeat;\n*GM\nid \
Der(f?boson(i?))*GM=-GM*GammaM(f(i))*GM+GM*Der(f(i));\nid \
Der(f?fermions(i?))*GM=-etaM*GM*etaM*GammaM(f(i))*GM+etaM*GM*etaM*Der(f(i));\n\
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Der(f?fermions(i?))*dtRM=etaM*dtRM*etaM*Der(f(i));\n*id Der(?b)*end=0;\nid \
Der(?b)*dtRM=0;\n\n*GammaM\nid \
Der(f?boson(i?))*GammaM(?a)=GammaM(f(i),?a)+GammaM(?a)*Der(f(i));\nid \
Der(f?fermions(i?))*GammaM(?a)=GammaM(f(i),?a)+sign(?a)*etaM*GammaM(?a)*etaM*\
Der(f(i));\n\n*etaM\nid Der(?a)*etaM=etaM*Der(?a);\n\n*sign\nid \
Der(f1?(i1?))*sign(?a)=sign(?a)*Der(f1(i1));\n\nEndRepeat;\n\n*resolve signs\n\
Repeat;\nid sign(fphi?boson(i?))=1;\nid sign(fpsi?fermions(i?))=-1;\nid \
sign(fphi?boson(i?),?a)=sign(?a);\nid sign(fpsi?fermions(i?),?a)=-sign(?a);\n\
id sign()=1;\nEndRepeat;\n\n* remove etaM squares\nRepeat;\nid etaM*etaM=1;\n\
EndRepeat;\n\n*remove end markers\nid end=1;\n.sort\n\n\
******************************************************************************\
**\n* already set vertices to zero before inserting propagators (field \
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******************************************************************************\
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nfF?Gmatrix=Trnc(nfF);\nrepeat id Trnc(?a)*Trnc(?b)=Trnc(?a,?b);\nid \
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******************************************************************************\
**\n*for the case of no derivatives\nid \
Tr(G(f1?(ix1?),f2?(ix2?)),dtR(f3?fermion(ix2?),f4?afermion(ix1?)))=Tr(G(f2(\
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is reached first\n#do iext=1,`EXTFIELDS'\n*reverse Tr only if smallest ext \
index is found in the other direction \n*or fermionic tadpole with regulator \
not in canonical order\n\
if(match(Tr(?a1,Gamma(?a2,f1?(i`iext'),?a3),G(?a4),dtR(f2?(i2?),f3?(i3?)),G(?\
a6),Gamma(?a7)))||match(Tr(G(?a),dtR(f3?fermion(ix2?),f4?afermion(ix3?)),G(?b)\
,Gamma(?c)))||match(Tr(G(?a),Gamma(?c),G(?b),dtR(f3?fermion(ix2?),f4?afermion(\
ix3?)))));\nTransform,Tr,reverse(1,last);\nArgument;\nid \
fG?GammadtRG(?a,f1?fermions(i1?),f2?fermions(i2?))=-fG(?a,f2(i2),f1(i1));\nid \
fG?GammadtRG[n](?a,f1?boson(i1?),f2?fermions(i2?))=GammadtRG2[n](?a,f2(i2),f1(\
i1));\nid \
fG?GammadtRG[n](?a,f1?fermions(i1?),f2?boson(i2?))=GammadtRG2[n](?a,f2(i2),f1(\
i1));\nid fG?GammadtRG(?a,f1?boson(i1?),f2?boson(i2?))=fG(?a,f2(i2),f1(i1));\n\
Endargument;\nFactarg Tr;\nrepeat id Tr(n?number_,?a)=n*Tr(?a);\nid \
Tr(?d,dtR(?a),G(?b),Gamma(?c))=Tr(?d,dtR(?a),G(?b),Gamma2(?c));\nelse;\nid \
Tr(?a1,dtR(?a2),G(?a3),Gamma(?a4,f1?(i`iext'),?a5))=Tr(?a1,dtR(?a2),G(?a3),\
Gamma2(?a4,f1(i`iext'),?a5));\nendif;\n#enddo\n\nargument;\nid \
Gamma2(?a)=Gamma(?a);\nid dtR(?a)=current(dtR(?a));\nendargument;\n\n*rename \
all dummy indices to iint\n#do iext=1,{2*`EXTFIELDS'+2}\nid  \
Tr(?a,current(fG1?(?b,f1?(i1?),f2?(i2?))),fG2?(?c,f3?(i2?),f4?(i3?)))=Tr(?a,\
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Tr(?a,current(dtR(?b)))=Tr(?a,dtR(?b));\n#enddo\n\n\
******************************************************************************\
**\n**************************************************************************\
******\n* remove Tr\nchainout Tr;\nrepeat id Tr(f1?(?a))=f1(?a);\n\n* bring \
vertices and dtR and propagators in canonical order (field-dep)\nRepeat;\n* \
general reordering first bosons then afermions then fermions\nid \
fG?GammadtRG(?a,f1?fermions(i1?),f2?boson(i2?),?b)=fG(?a,f2(i2),f1(i1),?b);\n\
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*)

(* End of internal cache information *)