A short introduction to the quantum formalism[s]. (arXiv:1211.5627v1 [math-ph])

A short introduction to the quantum formalism[s]. (arXiv:1211.5627v1 [math-ph]):
These notes are an elaboration on: (i) a short course that I gave at the
IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in
quantum mechanics. They present an introductory, but hopefully coherent, view
of the main formalizations of quantum mechanics, of their interrelations and of
their common physical underpinnings: causality, reversibility and
locality/separability. The approaches covered are mainly: (ii) the canonical
formalism; (ii) the algebraic formalism; (iii) the quantum logic formulation.
Other subjects: quantum information approaches, quantum correlations,
contextuality and non-locality issues, quantum measurements, interpretations
and alternate theories, quantum gravity, are only very briefly and
superficially discussed. Most of the material is not new, but is presented in
an original, homogeneous and hopefully not technical or abstract way. I try to
define simply all the mathematical concepts used and to justify them
physically. These notes should be accessible to young physicists (graduate
level) with a good knowledge of the standard formalism of quantum mechanics,
and some interest for theoretical physics (and mathematics). These notes do not
cover the historical and philosophical aspects of quantum physics.