Related papers: On the problem of interactions in quantum theory
As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…
Space-time measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about space-time is in fact an assertion…
The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter…
The paper contains a complete theory of factors for ray representations acting in a Hilbert bundle, which is a generalization of the known Bargmann's theory. With the help of it we have reformulated the standard quantum theory such that the…
The structure of the state spaces of bipartite (N tensor N) quantum systems which are invariant under product representations of the group SO(3) of three-dimensional proper rotations is analyzed. The subsystems represent particles of…
Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum…
We describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
In quantum theory, real degrees of freedom are usually described by operators which are self-adjoint. There are, however, exceptions to the rule. This is because, in infinite dimensional Hilbert spaces, an operator is not necessarily…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
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…
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a…
Recently, a bundle theoretic description of massive single-particle state spaces, which is better suited for Relativistic Quantum Information Theory than the ordinary Hilbert space description, has been suggested. However, the mathematical…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous…