Fixed a bug in DOTSimplify related to the separation

of Dirac and color structures (Issue #168, thanks to QSSRHelper)
FeynCalc · Apr 17, 2022 · a1fd68d · a1fd68d
1 parent 93bf601
commit a1fd68d
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diff --git a/FeynCalc/NonCommAlgebra/DotSimplify.m b/FeynCalc/NonCommAlgebra/DotSimplify.m
@@ -383,24 +383,41 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \
 		(* Dirac, Pauli and SU(N) matrices commute with each other, so they need to be properly separated*)
 		If[ !FreeQ2[x, {SUNT,PauliSigma,PauliEta,PauliXi}],
 			time=AbsoluteTime[];
-			FCPrint[1, "DotSimplify: Pulling out SU(N) matrices", FCDoControl->dsVerbose];
 			x  = x /. DOT->holdDOT;
-			(* Notice that here we are checking heads, so this will not break a possibly complicated nested structure *)
+			(*
+				Notice that even though we are checking heads here, one could still possibly mess up
+				some complicated nested structure. This could happend if the option Expanding has been
+				set to False so that we have DOTs inside DOTs.
 
-			x = x //. holdDOT[zzz__] :> (holdDOTColor@@Select[{zzz}, (Head[#] === SUNT) &])(holdDOTRest1@@Select[{zzz}, (Head[#] =!= SUNT) &]);
-			FCPrint[1, "DotSimplify: Pulling out Dirac matrices", FCDoControl->dsVerbose];
+				To avoid this situation, DOTs with nested must be left untouched. Otherwise, something like
+
+				GAD[mu] . SUNT[a] . (SUNT[cola, colb] .  GAD[nu]) . (SUNT[colc] . GAD[rho] . GSD[x] + SUNT[colc] . GSD[y] . GAD[rho] . GAD[lorf])
 
+				turns into
+
+				GAD[mu] . GAD[nu] . (GAD[rho] . GSD[x] SUNT[colc] + GSD[y] . GAD[rho] . GAD[lorf] SUNT[colc]) SUNT[a] . SUNT[cola] . SUNT[colb]
+
+				where the color structure gets messed up!
+			*)
+			FCPrint[1, "DotSimplify: Pulling out SU(N) matrices", FCDoControl->dsVerbose];
+			x = x //. holdDOT[zzz__]/; FreeQ2[{zzz}, {holdDOT, holdDOTColor}] :>
+				(holdDOTColor@@Select[{zzz}, (Head[#] === SUNT) &])(holdDOTRest1@@Select[{zzz}, (Head[#] =!= SUNT) &]);
+			FCPrint[3, "DotSimplify: After pulling out SU(N) matrices:", x, FCDoControl->dsVerbose];
+
+			FCPrint[1, "DotSimplify: Pulling out Dirac matrices", FCDoControl->dsVerbose];
 			x = x //. holdDOTRest1[zzz__] :> (holdDOTDirac@@Select[{zzz}, !FreeQ2[{#},{DiracGamma,Spinor}]& ])*
 			(holdDOTRest2@@Select[{zzz}, FreeQ2[{#},{DiracGamma,Spinor}]& ]);
-			FCPrint[1, "DotSimplify: Pulling out Pauli matrices", FCDoControl->dsVerbose];
+			FCPrint[3, "DotSimplify: After pulling out Dirac matrices: ", x, FCDoControl->dsVerbose];
 
+			FCPrint[1, "DotSimplify: Pulling out Pauli matrices", FCDoControl->dsVerbose];
 			x = x //. holdDOTRest2[zzz__] :> (holdDOTPauli@@Select[{zzz}, !FreeQ2[{#},{PauliSigma,PauliEta,PauliXi}]& ])*
 			(holdDOTRest3@@Select[{zzz}, FreeQ2[{#},{PauliSigma,PauliEta,PauliXi}]&]);
+			FCPrint[3, "DotSimplify: After pulling out Pauli matrices: ", x, FCDoControl->dsVerbose];
 
 			(* SUNT's and PauliSigma's in a DiracTrace are pulled out but NOT summed over *)
 			x = x //. DiracTrace[f_ g :(_holdDOTColor | _holdDOTPauli ) ] :> g DiracTrace[f]/.
-			(holdDOTColor|holdDOTDirac|holdDOTPauli|holdDOTRest1|holdDOTRest2|holdDOTRest3)[] -> 1  /.
-			holdDOTColor|holdDOTDirac|holdDOTPauli|holdDOTRest1|holdDOTRest2|holdDOTRest3 -> DOT;
+			(holdDOT|holdDOTColor|holdDOTDirac|holdDOTPauli|holdDOTRest1|holdDOTRest2|holdDOTRest3)[] -> 1  /.
+			holdDOT|holdDOTColor|holdDOTDirac|holdDOTPauli|holdDOTRest1|holdDOTRest2|holdDOTRest3 -> DOT;
 			FCPrint[1, "DotSimplify: Done pulling out all matrices, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose];
 			FCPrint[3, "DotSimplify: After pulling out all matrices: ", x,  FCDoControl->dsVerbose]
 		];

diff --git a/Tests/Dirac/DiracSimplify.test b/Tests/Dirac/DiracSimplify.test
@@ -227,7 +227,28 @@ Spinor[-Momentum[p1, D], mb, 1].GAD[i1].GAD[i2].GAD[i3].GAD[i4].GAD[
 "{GA[mu] SP[p, p], 2 FV[p, mu] GS[p] - GA[mu] SP[p, p]}"},
 {"fcstDiracSimplify-ID46",
 "DiracSimplify[GAD[mu].(GSD[p + q] + m).GAD[mu],FCE->True]",
-"D m + 2 GSD[p] - D GSD[p] + 2 GSD[q] - D GSD[q]"}
+"D m + 2 GSD[p] - D GSD[p] + 2 GSD[q] - D GSD[q]"},
+
+{"fcstDiracSimplify-ID49",
+"DiracTrace[
+GAD[\[Mu]] . GA[5] . SUNT[a] . SUNT[cola, colb] . GAD[lorc] .
+	GSD[x] . GAD[lord] . GAD[\[Nu]] .
+	GA[5] . (SUNT[colc] . FVD[x, lore] . GAD[lorf] +
+	SUNT[colc] . GAD[lore] . GAD[lorf] . GSD[x]) MTD[lorc,
+	lore] MTD[lord, lorf] SUNF[cola, colb, colc]] //
+DiracSimplify[#, FCE -> True] &",
+"64 SUNT[a] . SUNT[cola] . SUNT[colb] . SUNT[colc] FVD[x, \[Mu]] FVD[
+x, \[Nu]] SUNF[cola, colb, colc] -
+48 D SUNT[a] . SUNT[cola] . SUNT[colb] . SUNT[colc] FVD[
+x, \[Mu]] FVD[x, \[Nu]] SUNF[cola, colb, colc] +
+8 D^2 SUNT[a] . SUNT[cola] . SUNT[colb] . SUNT[colc] FVD[
+x, \[Mu]] FVD[x, \[Nu]] SUNF[cola, colb, colc] -
+40 SUNT[a] . SUNT[cola] . SUNT[colb] .
+SUNT[colc] MTD[\[Mu], \[Nu]] SPD[x, x] SUNF[cola, colb, colc] +
+28 D SUNT[a] . SUNT[cola] . SUNT[colb] .
+SUNT[colc] MTD[\[Mu], \[Nu]] SPD[x, x] SUNF[cola, colb, colc] -
+4 D^2 SUNT[a] . SUNT[cola] . SUNT[colb] .
+SUNT[colc] MTD[\[Mu], \[Nu]] SPD[x, x] SUNF[cola, colb, colc]"}
 };
 
 

diff --git a/Tests/NonCommAlgebra/DotSimplify.test b/Tests/NonCommAlgebra/DotSimplify.test
@@ -121,5 +121,31 @@ DotSimplify[ExpandPartialD[QuantumField[A1].QuantumField[A1].LeftPartialD[nu]]]"
 {"fcstDotSimplify-ID24","AntiCommutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A2], QuantumField[A2]] = 0;
 DotSimplify[ExpandPartialD[QuantumField[A2].QuantumField[A2].LeftPartialD[nu]]]","0"},
 {"fcstDotSimplify-ID25","DotSimplify[DCHN[GA[mu].(x GS[p]).GA[nu], i, j], FCE -> True]",
-"x DCHN[GA[mu].GS[p].GA[nu], i, j]"}
+"x DCHN[GA[mu].GS[p].GA[nu], i, j]"},
+{"fcstDotSimplify-ID26","DotSimplify[
+GAD[mu] . SUNT[a] . (SUNT[cola, colb] . GAD[nu]) . (SUNT[colc] . GAD[rho] . GSD[x] +
+	SUNT[colc] . GSD[y] . GAD[rho] . GAD[lorf]), Expanding -> False,
+FCE -> True]",
+"GAD[mu] . SUNT[a] . SUNT[cola] . SUNT[colb] .
+GAD[nu] . (GAD[rho] . GSD[x] SUNT[colc] +
+GSD[y] . GAD[rho] . GAD[lorf] SUNT[colc])"},
+
+{"fcstDotSimplify-ID27","DotSimplify[
+DiracGammaCombine[
+DiracTrace[
+MTD[lord, lorf] MTD[lorc, lore] SUNF[cola, colb,
+	colc] GAD[\[Mu]] . GA[5] .
+	SUNT[a] . (SUNT[cola, colb] . GAD[lorc] . GSD[x] . GAD[lord]) .
+	GAD[\[Nu]] .
+	GA[5] . (SUNT[colc] . GAD[lore, lorf] . GSD[x] +
+	SUNT[colc] . FVD[x, lore] . GAD[lorf])]], Expanding -> False,
+FCE -> True]",
+"DiracTrace[
+GAD[\[Mu]] . GA[5] . SUNT[a] . SUNT[cola] . SUNT[colb] . GAD[lorc] .
+GSD[x] . GAD[lord] . GAD[\[Nu]] .
+GA[5] . (GAD[lore] . GAD[lorf] . GSD[x] SUNT[colc] +
+	 FVD[x, lore] GAD[lorf] SUNT[colc]) MTD[lorc, lore] MTD[lord,
+lorf] SUNF[cola, colb, colc]]"}
+
+
 }
diff --git a/Tests/SUN/SUNTrace.test b/Tests/SUN/SUNTrace.test
@@ -31,6 +31,12 @@ Tests`SUN`fcstSUNTraceColorTraces = {
 {"fcstSUNTraceColorTraces-ID8","SUNTrace[SUNF[a, r, s] SUNF[b, r, s]] // SUNSimplify",
 	"CA^2*SUNDelta[SUNIndex[a], SUNIndex[b]]"},
 {"fcstSUNTraceColorTraces-ID9","SUNTrace[SUNT[a, b, c, a, b, c]]",
-	"-(1/(8 SUNN^2)) + SUNN^2/8"}
+	"-(1/(8 SUNN^2)) + SUNN^2/8"},
+{"fcstSUNTraceColorTraces-ID10","SUNTrace[GAD[\[Mu]] . GA[5] . SUNT[a] . SUNT[cola, colb] .
+GAD[lorc] . GSD[x] . GAD[lord] . GAD[\[Nu]] .
+GA[5] . (SUNT[colc] . FVD[x, lore] . GAD[lorf] +
+	SUNT[colc] . GAD[lore] . GAD[lorf] . GSD[x]) MTD[lorc, lore] MTD[
+lord, lorf] SUNF[cola, colb, colc]]",
+	"0"}
 };