note on notation and choice of indices

examples of Poisson-Bracket notation: 
  *  [(d)]
  *  [(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]
  * [Sussman] calls the superscript indices "traditional"
  * Indexing is usually (almost universally) zero-based. 


-- 24.xi.2008

refs: (of the better/more detailed discussions on indices)

[Aitchison] Gauge theories in particle physics volume 1, 3rd ed.
[Shankar] R. Shankar, Principles of quantum mechanics, 2ed., Yale UP 1992/4.
[Siegel] Warren Siegel, Fields.
[Srednicki] Srednicki, Quantum Field Theory, (c) 2006 , \\ [[http://www.physics.ucsb.edu/~mark/qft.html|book website]]
[Sussman] [Sussman 2001] Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer, Structure and Interpretation of Classical Mechanics, The MIT Press Cambridge, Massachusetts, 2001,
http://www-swiss.ai.mit.edu/~gjs/6946/sicm-html/book.html , retrieved 08 aug 2006, 20 nov 2007 and nov/dec 2008.