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In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…

The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…

In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a…

Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation…

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…

Elementary particles are found in two different situations: (i) bound to metastable states of matter, for which angular momentum is quantized, and (ii) free, for which, due to their high energy-momentum and leaving aside inner a.m. or spin,…

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…

It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…

In this paper, we develop a formalism describing in a relativistic way a system which consists of a classical and a quantum part being coupled. The formalism models one particle with spin 1/2 and it is a possible relativistic extension of…

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…

The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…

A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…

The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of Kronecker product and what we have termed the `bra-flipper' operator.…

Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…

In quantum electrodynamics, optical processes are theoretically described by double-sided Feynman diagrams. This formalism is powerful in the case of molecules but proves inappropriate to account for light-matter interactions within complex…

We review some quantum-phase descriptions of optical fields. We focus on real fields that can be generated in practice in various nonlinear optical processes. Thus, we rather avoid discussions of phase formalisms as such and try to exploit…

After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics…

Classical electromagnetic fields and quantum mechanics -- both obey the principle of superposition alike. This opens up many avenues for simulation of a large variety of phenomena and algorithms, which have hitherto been considered quantum…

We continue in this paper our program of rederiving all quantum mechanical formalism from the classical one. We now turn our attention to the derivation of the second quantized equations, both for integral and half-integral spins. We then…