Dear all, I found out that canonicalizing clifford objects was not functioning properly. This was because a dirac_slash was automatically getting zero as its metric. When canonicalizing clifford objects the anti-commutator of two objects that were ordered in the wrong way is necesary. However, if the metric is automatically set to zero, this anti-commutator is zero too. I fixed this in CVS. I do have two questions about the implementation (1) Why are the indices in dirac_gamma (and with my patch in dirac_slash) static? Does the dimension of them not matter? It now seems that the dimension as used in the metric is always equal to the dimension of the very first dirac_gamma/dirac_slash that is constructed. (2) Why does the metric have indices? In view of the implementation of get_metric the primary purpose of these indices seems to be to be replaced by other indices. If that is the case why are they present in the first place? Best, Chris
I cannot say anything about dirac_slash, thus here are some comments on the second topic:
"CD" == Chris Dams <Chris.Dams@mi.infn.it> writes: CD> (2) Why does the metric have indices?
It will be nice to combine two things: (a) to standardise storage of metric to an object of certain type; (b) to have a freedom to define metric from many different objects like matrices or tensors. Thus indexed object is chosen as a standard storage for a metric with its first component to hold actual metric (e.g. matrix or tensor). Indices are indeed somehow superficial but having some default values for them seems to be useful for example in same_metric(). Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv@maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/
Dear Vladimir, On Wed, 4 Jan 2006, Vladimir Kisil wrote:
Thus indexed object is chosen as a standard storage for a metric with its first component to hold actual metric (e.g. matrix or tensor). Indices are indeed somehow superficial but having some default values for them seems to be useful for example in same_metric().
However, also in same_metric, get_metric is called and that replaces the indices. So maybe there is an example in which the indices serve a purpose but it does not seem to be in the same_metric function. The alternative that would seem to be more logic is to store the thing that should take the indices. For instance a matrix or a minkmetric. In that case get_metric would not have to substitute indices but could merely return indexed(metric, i, j). Is the purpose of having the metric inside an indexed object to also store the symmetry of the metric? Best wishes, Chris
"CD" == Chris Dams <Chris.Dams@mi.infn.it> writes:
CD> However, also in same_metric, get_metric is called and that CD> replaces the indices. Currently same_metric replaces the indices with indices from the metric of another clifford object (assuming that they are present). CD> indexed(metric, i, j). Is the purpose of having the metric CD> inside an indexed object to also store the symmetry of the CD> metric? Yes, this is another important reason which I forgot to mention. Besides that the presence of indeces keep record on the dimensionality of the Clifford algebra. Otherwise it need to be stored separately if the metric is given for example by minkmetric. Overall keeping metric as indexed object can provide some important info on generic Clifford algebra which otherwise would be lost. Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv@maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/
participants (2)
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Chris Dams
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Vladimir Kisil