p-Mechanics and De Donder-Weyl Theory

The orbit method of Kirillov is used to derive the p-mechanical brackets [quant-ph/0212101]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder-Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with Galilean. Keywords: Classic and quantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, deformation quantisation, representation theory, De Donder-Weyl field theory, Galilean group, Clifford algebra, conformal M\"obius transformation, Dirac operatorComment: LaTeX, 8 pages, no figure

Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity

We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In addition to the usual $\star$-product deformation of the algebra of field functions, we show that the parameter of noncommutativity can occur in noncommutative field theory even in the case of free fields without self-interacting potentials.Comment: 13 page

Do We Understand Quantum Mechanics - Finally?

After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator algebras. We then review some basic aspects of quantum mechanics and, in particular, of its interpretation. We attempt to clarify what Quantum Mechanics tells us about Nature when appropriate experiments are made. We discuss the importance of the mechanisms of "dephasing" and "decoherence" in associating "facts" with possible events and rendering complementary possible events mutually exclusive.Comment: 42 pages, contribution to the Proceedings of a conference in memory of Erwin Schroedinger, Vienna, January 201