相关论文: Framed Hilbert space: hanging the quasi-probabilit…

A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…

The Hilbert space structure of classical field theory is proposed as a general theoretical framework to model human cognitive processes which do not often follow classical (Bayesian) probability principles. This leads to an extension of the…

An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert…

A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…

These are the notes written for the talk given at the workshop Rethinking foundations of physics 2016. In section 2, a derivation of the the quantum formalism starting from propositional calculus (quantum logic) is reviewed, pointing out…

There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…

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…

In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…

The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…

The physical world is quantum. However, our description of the quantum physics still relies much on concepts in classical physics and in some cases with `quantized' interpretations. The most important case example is that of spacetime. We…

We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…

Instead of formulating the states of a Quantum Field Theory (QFT) as density matrices over a single large Hilbert space, it has been proposed by Kijowski [Kijowski, 1977] to construct them as consistent families of partial density matrices,…

We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…

We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…

Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry…

The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures…

We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant…

An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a…