From fd6bfb8ca9a7f4bf52daf16d93d18aecc44e37e6 Mon Sep 17 00:00:00 2001 From: Christian Bauer Date: Wed, 20 Nov 2002 20:34:30 +0000 Subject: [PATCH] documentation update (Clifford algebra) --- doc/tutorial/ginac.texi | 31 +++++++++++++++++-------------- 1 file changed, 17 insertions(+), 14 deletions(-) diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi index 54a37343..25340def 100644 --- a/doc/tutorial/ginac.texi +++ b/doc/tutorial/ginac.texi @@ -2381,28 +2381,29 @@ ex dirac_ONE(unsigned char rl = 0); multiples of the unity element, even though it's customary to omit it. E.g. instead of @code{dirac_gamma(mu)*(dirac_slash(q,4)+m)} you have to write @code{dirac_gamma(mu)*(dirac_slash(q,4)+m*dirac_ONE())}. Otherwise, -GiNaC may produce incorrect results. +GiNaC will complain and/or produce incorrect results. @cindex @code{dirac_gamma5()} -There's a special element @samp{gamma5} that commutes with all other -gammas and in 4 dimensions equals @samp{gamma~0 gamma~1 gamma~2 gamma~3}, -provided by +There is a special element @samp{gamma5} that commutes with all other +gammas, has a unit square, and in 4 dimensions equals +@samp{gamma~0 gamma~1 gamma~2 gamma~3}, provided by @example ex dirac_gamma5(unsigned char rl = 0); @end example -@cindex @code{dirac_gamma6()} -@cindex @code{dirac_gamma7()} -The two additional functions +@cindex @code{dirac_gammaL()} +@cindex @code{dirac_gammaR()} +The chiral projectors @samp{(1+/-gamma5)/2} are also available as proper +objects, constructed by @example -ex dirac_gamma6(unsigned char rl = 0); -ex dirac_gamma7(unsigned char rl = 0); +ex dirac_gammaL(unsigned char rl = 0); +ex dirac_gammaR(unsigned char rl = 0); @end example -return @code{dirac_ONE(rl) + dirac_gamma5(rl)} and @code{dirac_ONE(rl) - dirac_gamma5(rl)}, -respectively. +They observe the relations @samp{gammaL^2 = gammaL}, @samp{gammaR^2 = gammaR}, +and @samp{gammaL gammaR = gammaR gammaL = 0}. @cindex @code{dirac_slash()} Finally, the function @@ -2417,9 +2418,11 @@ with a unique index whose dimension is given by the @code{dim} argument). Such slashed expressions are printed with a trailing backslash, e.g. @samp{e\}. In products of dirac gammas, superfluous unity elements are automatically -removed, squares are replaced by their values and @samp{gamma5} is -anticommuted to the front. The @code{simplify_indexed()} function performs -contractions in gamma strings, for example +removed, squares are replaced by their values, and @samp{gamma5}, @samp{gammaL} +and @samp{gammaR} are moved to the front. + +The @code{simplify_indexed()} function performs contractions in gamma strings, +for example @example @{ -- 2.34.3