Re: [GiNaC-list] question about lorentz_g contract with sy_anti tensor
Thanks very for the reply. and I have tried the suggestion, i.e., using the following expression: auto ret = indexed(A, sy_anti(0,1,2,3), ia,ib,ic,id) * lorentz_g(ic, id.toggle_variance()); but I got something like: -delta.d~c*A~d~a~b~c, still a non-zero result. BTW, if c’s variance is not toggled in lorentz_g, then these two dummy index c’s variance is not matched, and is that allowed? Thanks again!
On Sat, 25 May 2019 14:57:54 +0000, Feng Feng <F.Feng@outlook.com> said:
FF> Thanks very for the reply. and I have tried the suggestion, FF> i.e., using the following expression: FF> auto ret = indexed(A, sy_anti(0,1,2,3), ia,ib,ic,id) * FF> lorentz_g(ic, id.toggle_variance()); FF> but I got something like: -delta.d~c*A~d~a~b~c, still a non-zero FF> result. It looks like you did not call simplified_indexed(). Please see attached code which outputs: Not-reduced: delta.d~c*A~b~a~d~c Anti-symmetry: 0 FF> BTW, if c’s variance is not toggled in lorentz_g, FF> then these two dummy index c’s variance is not matched, FF> and is that allowed? This is exactly what you obtain by lowering/raised just one index in the metric tensor itself: g_c^d = g_{ce} g^{ed}, see https://en.wikipedia.org/wiki/Metric_tensor -- Vladimir V. Kisil http://www.maths.leeds.ac.uk/~kisilv/ Book: Geometry of Mobius Transformations http://goo.gl/EaG2Vu Software: Geometry of cycles http://moebinv.sourceforge.net/
participants (2)
-
Feng Feng
-
Vladimir V. Kisil