------------------------------------------------------------------------
2007
3 Jan - First version of Spinors.nb. Chosen version number 0.3.0.
- xTensor modified to contract and canonicalize antisymmetric
metrics. Added option ExtendedFrom in DefCovD.
- DefSpinStructure.
23 Jan - Eliminated warning messages RuleDelayed::rhs produced by
DefSpinStructure.
16 Aug - Updated Spinors.nb for version 0.9.2 of xAct.
5 Oct - Eliminated the syntax of DefSpinStructure in which the user
supplies the explicit names of the epsilon tensor and the
soldering form. The reason for this is due to clashes between
the indices given by the user and those used internally by
DefSpinStructure.
- Added the option Master->Spin_structure_name in the definition
of the curvature spinors.
------------------------------------------------------------------------
2008
2 Jan - Changes in the tensor names assigned automatically by
DefSpinStructure. Some other minor changes.
4 Jan - Added Remove in the code of UndefSpinStructure in order to remove
the symbol representing the spin structure.
- Corrected a bug in Decomposition which arose when using the option
FRiemann.
9 Jan - Added PutSolderingForm and VBundleOfSolderingForm.
16 Jan - Introduced the spinor equivalent of the metric tensor. This spinor
is automatically replaced by a product of epsilon spinors.
9 May - PutSolderingForm broken in two parts. Default index arguments.
10 May - Lots of small changes for compatibility with latest xTensor/xCoba.
- Added derivatives with two indices using a generalized form of
MakeLinearDerivative in xTensor.
12 May - Added a type for spin derivatives
- ContractSolderingForm and SeparateSolderingForm can now handle
2-index derivatives.
15 Jul - The action of Dagger upon the Box differential operator is
declared by means of a downvalue, instead of an upvalue.
16 Jul - Introduced the commands BoxToCovD and BoxToCurvature.
17 Jul - Corrected a bug in the functions spindRules and tindRules.
18 Jul - DefSpinorOfTensor can now handle tensors which are complex
(if a tensor is complex and we define its spinor equivalent,
then we need to consider the spinor equivalent of the complex
conjugate tensor). This requires a modification in the code
of ContractSolderingForm in order to keep our convention
about index sorting.
6 Aug - Introduced the global variables $PhiSign, $ChiSign, $PsiSign
and $LambdaSign used to set the conventions in the definition
of the curvature spinors.
- $SolderingForms turned into a public variable.
- Changed the declaration of the automatic rules which give the
product of the tetra-metric with Sigma. In this way the number
of such rules is reduced.
7 Aug - Changed the formatting of the operator Boxcd in order to add
information about the covariant derivative cd.
10 Aug - Added the spinor equivalent of the volume element and its
automatic rule of decomposition into irreducible parts.
11 Aug * First public release, with version number 0.9.0.
24 Sep - Fixed wrong sign in the traces of Sigmasoldering.
2 Oct - Solved missing sign in contractions with sigma (SpinSign).
7 Oct - Fixed signs in products of sigma's giving Sigma.
16 Oct - Added IrreducibleDecomposition.
2 Nov - Added missing symmetries on the spinor Chi when it stems from the
Levi-Civita connection. Included also the case in which the
torsion is present.
- Added torsion spinor Omega. Changes in BoxToCurvature to include
the torsion and to make the expressions consistent with the
spinor form of the Ricci identities.
- DefSpinCovD accepts now the option Torsion->True.
- Added Posibility of definining spin structures on spacetimes with
torsion.
20 Nov - Fixed special case 0 in Put/Separate/ContractSolderingForm.
- SpinCovDs are now "Hermitian".
23 Nov - ContractSolderingForm acts through compatible derivatives.
1 Dec - Spinors.nb and SpinorsDoc.nb reexecuted and cleaned.
* Released with version number 0.9.1.
------------------------------------------------------------------------
2009
9 Sep - Documentation extended.
- File PublicNPGHP.nb with applications of Spinors to NP and GHP
separated from the main documentation file.
* Released with version number 0.9.2.
9 Dec - Fixed wrong sign conventions in the code of BoxToCurvature and
the code which computes the decomposition of the curvature spinor
Chi (DecompositionRules[covd,Chi]). Thanks to Thomas Bäckdahl for
spotting these mismatches. One needs to check the formulae in
BoxToCurvature when the torsion does not vanish (currently there
is a private function named $BoxTorsionSign which will show up when
the torsion does not vanish).
------------------------------------------------------------------------
2010
10 Jan * Rereleased with same version number 0.9.2.
22 Sep - Fixed wrong dummy index position in the contraction of the curvature
spinors Phi and Dagger@Phi when the torsion is non-zero (when the
torsion vanishes, this index position is irrelevant due to the
additional symmetries of Phi).
- Variable $BoxTorsionSign coincides with $TorsionSign, which replaces
it now.
- Fixed wrong results by the command BoxToCurvature when the torsion
does not vanish.
- Added command SortSpinCovDs which is the counterpart of SortCovDs for 2-index
spin covariant derivatives.
30 Sep * Released with version number 1.0.0.
------------------------------------------------------------------------
2011
11 Mar - Added definition for FirstDerQ on spin covds, as suggested by Thomas.
22 Mar - For some reason, there was an error message issued when DefSpinCovD was an
extension of the Levi-Civita covd of a frozen metric. This message no longer
exists.
23 Mar - When DefSpinCovD carries the option Curvature->False, then one cannot define
the curvature spinors. We included some checks in the rutine ConstructRTSpinors
to fix that.
17 Apr - SpinCovDQ made public.
* Released with version number 1.0.1.
23 Oct - Changed sign of the spinor form of the epsilon tensor, as suggested
by Thomas, to coincide with the conventions in Penrose & Rindler.
Currently it uses $epsilonTetraSign.
* Released with version number 1.0.2.
------------------------------------------------------------------------
2012
28 Apr - Fixed problem in SeparateSolderingForm with dagger tensors, found by Thomas.
- Added variable $xTensorVersionExpected to enforce the correct version.
- Changed $PsiSign convention to match Penrose & Rindler.
5 May * Released with version number 1.0.3.
------------------------------------------------------------------------
2013
26 Jan - TensorSymmetry renamed SymmetryOfTensor to avoid conflict with
Mathematica9.
27 Jan * Released with version number 1.0.4.
16 Mar - Use VBundleIndexQ and VBundleIndexPMQ to construct the `Q and `pmQ
functions.
-------------------------------------------------------------------------
2014
9 Jan - Corrected minor error in SpinCovDsOfSolderingForm pointed out by Thomas Bäckdahl.
The spin covariant derivative used in DefSpinStructure was repeated in the list generated
by SpinCovDsOfSolderingForm.
4 Feb - Corrected problem with non-existent options message issued by DefSpinStructure in relation to DefSpinCovD
Thanks to Thomas Bäckdahl for spotting this and providing the solution.
15 Feb * Released with version number 1.0.5.
25 Apr - Added Thomas's PrintDaggerAs option in DefSpinor
10 June - Fixed problem in PrintDaggerAs. Thanks to Thomas for reporting it.
18 June - Added built-in options AddBar, AddTilde and AddDagger for PrintDaggerAs. Thanks to
Thomas for supplying the code of these built-in options.
28 Sep * Released with version number 1.0.6.
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2015
23 Aug * Released again with version number 1.0.6.
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2016
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2017
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2018