Related papers: The Representation of Natural Numbers in Quantum M…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
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…
A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that $0s$ in a qubit string do not contribute to the value of a number. They serve only as place…
We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the…
Limitation of computational resources is considered as a universal principle that for simulation is as fundamental as physical laws are. It claims that all experimentally verifiable implications of physical laws can be simulated by the…
The mathematical structure of the sheaf of Dedekind real numbers $\RsubD(X)$ for a quantum system is discussed. The algebra of physical qualities is represented by an $O^{*}$ algebra $\mathcal M$ that acts on a Hilbert space that carries an…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
A C*-algebra formulation of Quantum Mechanics is derived from purely operational axioms in which the primary role is played by the "transformations" that the system undergoes in the course of an "experiment". The notion of the {\em adjoint}…
We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated…
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…
This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The…
We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science.…