From 09f0415b7442714ea9adae30872d151452185962 Mon Sep 17 00:00:00 2001 From: Christian Bauer Date: Thu, 5 Aug 2004 21:05:39 +0000 Subject: [PATCH] added variants of dirac_trace() and color_trace() that take the trace over more than one representation label by specifying a set or list of labels --- doc/tutorial/ginac.texi | 34 +++++++++++++++++++++------------- 1 file changed, 21 insertions(+), 13 deletions(-) diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi index 9c4d15ee..50e95ae9 100644 --- a/doc/tutorial/ginac.texi +++ b/doc/tutorial/ginac.texi @@ -3002,20 +3002,25 @@ for example @cindex @code{dirac_trace()} To calculate the trace of an expression containing strings of Dirac gammas -you use the function +you use one of the functions @example +ex dirac_trace(const ex & e, const std::set & rls, const ex & trONE = 4); +ex dirac_trace(const ex & e, const lst & rll, const ex & trONE = 4); ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4); @end example -This function takes the trace of all gammas with the specified representation -label; gammas with other labels are left standing. The last argument to +These functions take the trace over all gammas in the specified set @code{rls} +or list @code{rll} of representation labels, or the single label @code{rl}; +gammas with other labels are left standing. The last argument to @code{dirac_trace()} is the value to be returned for the trace of the unity -element, which defaults to 4. The @code{dirac_trace()} function is a linear -functional that is equal to the usual trace only in @math{D = 4} dimensions. -In particular, the functional is not cyclic in @math{D != 4} dimensions when -acting on expressions containing @samp{gamma5}, so it's not a proper trace. -This @samp{gamma5} scheme is described in greater detail in +element, which defaults to 4. + +The @code{dirac_trace()} function is a linear functional that is equal to the +ordinary matrix trace only in @math{D = 4} dimensions. In particular, the +functional is not cyclic in @math{D != 4} dimensions when acting on +expressions containing @samp{gamma5}, so it's not a proper trace. This +@samp{gamma5} scheme is described in greater detail in @cite{The Role of gamma5 in Dimensional Regularization}. The value of the trace itself is also usually different in 4 and in @@ -3177,16 +3182,19 @@ expressions containing color objects: @end example @cindex @code{color_trace()} -To calculate the trace of an expression containing color objects you use the -function +To calculate the trace of an expression containing color objects you use one +of the functions @example +ex color_trace(const ex & e, const std::set & rls); +ex color_trace(const ex & e, const lst & rll); ex color_trace(const ex & e, unsigned char rl = 0); @end example -This function takes the trace of all color @samp{T} objects with the -specified representation label; @samp{T}s with other labels are left -standing. For example: +These functions take the trace over all color @samp{T} objects in the +specified set @code{rls} or list @code{rll} of representation labels, or the +single label @code{rl}; @samp{T}s with other labels are left standing. For +example: @example ... -- 2.31.1