09 December 2008

note on notation and choice of indices





examples of Poisson-Bracket notation:
* Poisson-Bracket notation on german wikipedia page [(d)]
* Poisson-Bracket notation on french wikipedia page [(f)]
* note how version (f) opts for supercripted indices for one set of canonical
coords. and subscripted for the other, while the (d) equivalent chooses
the simpler notation with all indices subscripted.
* In [Siegel] [Srednicki] [Aitchison] and others there are discussions on the
importance of the choice of indexing scheme used in the QFT commutator formalism
- which is already so complicated (;;) .
* Notation in another version (r) uses square brackets for the PB on the LHS,
eg. [f,g] , thus making it indistinguishable from the notation used to designate
the related quantum commutator, the Lie Bracket [a,b]. (Cf. introduction of the
commutator in [Shankar])
* Indeed in __Fields__, Siegel devotes §§A,B in the Symmetry chapter to
"Coordinates" and "Indices" resp. [Siegel]

-- 24.xi.2008

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