Classical mechanics is formulated in Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of sem...

I usually do not go to conferences which have in the title the standard fashionable words ”Quantum Gravity” (QG). I made an exception this time because my dear friend Giampiero had the good taste of creating two sessions: one dedicated to QG and another to ”Foundations of Quantization”(FQ). In fact I belong to that minority which thinks that we should not only try to attack the second of the tw...

Ġ = {G,H}. In particular, the DV F is called an integral if it has zero PB with the Hamiltonian {F,H} = 0. In this case F does not depend on t. In many problems of the classical mechanics DV form elegant algebraic structures which are closed with respect to PB. The Poisson structures with non-linear PB were discussed in [9] and [6]. Sklyanin introduced [9] the so-called quadratic Poisson algebr...

A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects. 1. Why Scaling, and why the given Groups ? Dimensional Analysis, Bluman & Kumei, is one of those fundamental aspects of Classical Physics which, nevertheless, is often left outside of one’s awaren...

It is shown that for a central potential that is an injective function of the radial coordinate, a second central potential can be found that leads to trajectories in the configuration space and the momentum space coinciding, respectively, with the trajectories in the momentum space and the configuration space produced by the original potential. Se muestra que para un potencial central que sea ...