Related papers: Quaternionic quantum mechanics in real Hilbert spa…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
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,…
As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and…
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…
The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical…
We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…