[GiNaC-list] question about lorentz_g contract with sy_anti tensor
Vladimir V. Kisil
kisilv at maths.leeds.ac.uk
Sat May 25 17:27:25 CEST 2019
>>>>> On Sat, 25 May 2019 14:57:54 +0000, Feng Feng <F.Feng at 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/
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