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Some basic concepts concerning systems of identical particles are discussed in the framework of a realist interpretation, where the wave function is the quantum object and |psi(r)|^2 d^3r is the probability that the wave function causes an…

We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…

Generalized contextuality refers to our inability of explaining measurement statistics using a context-independent probabilistic and ontological model. On the other hand, measurement statistics can also be modeled using the framework of…

This paper presents a detailed analysis of the pseudocontact shift (PCS) field induced by a mobile spin label that is viewed as a probability density distribution with an associated effective magnetic susceptibility anisotropy. It is…

The investigation of arXiv 1409.2766v2 [quant-ph] has been continued by the general form of the numerous equations with partial values of arbitrary spin, which were considered in above mentioned preprint. The general forms of…

We discuss the Full Counting Statistics of non-commuting variables with the measurement of successive spin counts in non-collinear directions taken as an example. We show that owing to an irreducible detector back-action, the FCS in this…

We consider the operator product expansion for quantum field theories on general analytic 4-dimensional curved spacetimes within an axiomatic framework. We prove under certain general, model-independent assumptions that such an expansion…

We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…

A model, based on a noncommutative geometry, unifying general relativity with quantum mechanics, is further develped. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators. It is…

We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the…

The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…

In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…

The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…

A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit existence of the non-relativistic limit in the covariant Dirac equation. Procedure…

All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…

A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…

We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…

Recently a new attempt to go beyond quantum mechanics (QM) was presented in the form of so called prequantum classical statistical field theory (PCSFT). Its main experimental prediction is violation of Born's rule which provides only an…

A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…