Related papers: Noncommutative quantum mechanics as a constrained …
In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the…
Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation…
Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special…
There are two different and logically independent concepts of noncontextuality in quantum mechanics. First, an ontological (hidden variable) model for quantum mechanics is called noncontextual if every ontic (hidden) state determines the…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the…
A quaternionic version of Quantum Mechanics is constructed using the Schwinger's formulation based on measurements and a Variational Principle. Commutation relations and evolution equations are provided, and the results are compared with…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations.
We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…