相关论文: An algebraic formulation of nonassociative quantum…

These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…

In [14] we introduced a new class of algebras, which we named \textit{quantum generalized Heisenberg algebras} and which depend on a parameter $q$ and two polynomials $f,g$. We have shown that this class includes all generalized Heisenberg…

We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…

It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…

Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…

Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…

A quantum system can be entirely described by the K\"ahler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we…

We describe a categorical model of MALL (Multiplicative Additive Linear Logic) inspired by the Heisenberg-Schr\"odinger duality of finite-dimensional quantum theory. Proofs of formulas with positive logical polarity correspond to CPTP…

Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra…

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…

Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…

The purpose of this contribution is to provide an introduction for a general physics audience to the recent results of Emile Grgin that unifies quantum mechanics and relativity into the same mathematical structure. This structure is the…

This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…

Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures. A synaptic algebra is a…

We deal with the general structure of (noncommutative) stochastic processes by using the standard techniques of Operator Algebras. Any stochastic process is associated to a state on a universal object, i.e. the free product $C^*$-algebra in…

We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…

A concise study of ternary and cubic algebras with $Z_3$ grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, $S_3$, and its abelian subgroup…

Many quantum groups and quantum spaces of interest can be obtained by cochain (but not cocycle) twist from their corresponding classical object. This failure of the cocycle condition implies a hidden nonassociativity in the noncommutative…

We examine certain nonassociative deformations of quantum mechanics and gravity in three dimensions related to the dynamics of electrons in uniform distributions of magnetic charge. We describe a quantitative framework for nonassociative…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…