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p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
We show a hitherto unexplored consequence of the property of identicity in quantum mechanics. If two identical objects, distinguished by a dynamical variable A, are in certain entangled states of another dynamical variable B, then, for such…
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the…