Related papers: Fock's theory of hydrogen atom and quantum space
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
The fuzzy onion model formed by connecting a set of concentric fuzzy spheres of increasing radius is motivated by studies of quantum space but can also be used to study standard physics. The main feature of the model is that functions in…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
I revisit the Wigner (or Weyl-Wigner, WW) representation of the quantum electromagnetic field. I show that, assuming that Fock states are just mathematical concepts devoid of physical reality, WW suggests a realistic interpretation which…
We show that the dynamical symmetry of the hydrogen atom leads in a natural way to an infinite-dimensional algebra, which we identify as the positive subalgebras of twisted Kac-Moody algebras of $ so(4)$. We also generalize our results to…
The wave-particle duality of the vacuum states of quantum fields is considered and the particle-like property of the vacuum state of a quantum field is proposed as a vacuum-particle which carries the vacuum-energy and the vacuum-momentum of…
A semi-classical reasoning leads to the non-commutativity of space and time coordinates near the horizon of static non-extreme black hole, and renders the classical horizon spreading to {\it Quantum Horizon} . In terms of the background…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
The concept of definability of quantum fields in a set-theoretical foundation is introduced. We propose an axiomatic set theory and then derive a nonlinear sigma model and the Schroedinger equation in a Lagrangian form; this follows…
The quantum algebra suq(2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of $q$-bosons. In connection with the quantum algebra suq(2), we discuss the q-analogues of the…
This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
We give a pedagogical introduction to algebraic quantum field theory (AQFT), with the aim of explaining its key structures and features. Topics covered include: algebraic formulations of quantum theory and the GNS representation theorem,…
We develop a non-relativistic quantum field theory of electrons and nuclei based on the Coulomb Hamiltonian. We derive the exact equations of motion and write these equations in the form of Hedin's equations for all species of identical…
A variation of the Zamolodchikov-Faddeev algebra over a finite dimensional Hilbert space $\mathcal{H}$ and an involutive unitary $R$-Matrix $S$ is studied. This algebra carries a natural vacuum state, and the corresponding Fock…
Understanding quantum theory in terms of a geometric picture sounds great. There are different approaches to this idea. Here we shall present a geometric picture of quantum theory using the de-Broglie--Bohm causal interpretation of quantum…
A new type of a nonlinear gauge quantum theory (superrelativity) has been proposed. Such theory demands a radical reconstruction of both the quantum field conception and spacetime structure, and this paves presumably way to the…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…