相关论文: Bringing Up a Quantum Baby

Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…

Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…

Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible…

We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…

Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…

In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…

The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…

In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…

The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…

The aim of the present paper is to introduce and to discuss the most basic fundamental concepts of quantum physics by means of a simple and pedagogical example. An appreciable part of its content presents original results. We start with the…

This paper starts by describing the dynamics of the electron-monopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are…

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to 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,…

The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. Do these abstract basis-independent objects give a complete description of the physical world, or should we include observables like positions and…

The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…

It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion…

We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…

Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular…