Related papers: Unitary Inequivalent Representations and Quantum P…
In connection with the contribution "Quantum Condensates in Nuclear Matter" some problems are given to become more familiar with the techniques of many-particle physics.
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
I discuss different formulations of the relativistic few-body problem with an emphasis on how they are related. I first discuss the implications of some of the differences with non-relativistic quantum mechanics. Then I point out that the…
The purpose of this article is to give a short introduction to the concept of quasi-unitary equivalence of quadratic forms and its consequences. In particular, we improve an estimate concerning the transitivity of quasi-unitary equivalence…
The generalization of the imaginary unit is examined within the instances of the complex quantum mechanics ($\mathbb C$QM), and of the quaternionic quantum mechanics ($\mathbb H$QM) as well. Whereas the complex theory describes…
We critically review the recent debate between Doreen Fraser and David Wallace on the interpretation of quantum field theory, with the aim of identifying where the core of the disagreement lies. We show that, despite appearances, their…
Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position -supported by E. Schrodinger- asserting that elementary particles are not individuals. But the subject goes deeper, and…
Representation of the quantum measurement with the help of non-orthogonal decomposition of unit is presented in the paper for the first time. Methods for solution of the quantum detection and measurement problems based on the suggested…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
The ``unification'' of fundamental physical forces (interactions) imagines a ``single'' conceptual entity using which {\em all} the observable or physical phenomena, {\em ie}, changes to physical bodies, would be suitably describable. The…
Simulating the dynamics of non-equilibrium matter under extreme conditions lies beyond the capabilities of classical computation alone. Remarkable advances in quantum information science and technology are profoundly changing how we…
We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.
The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined.
Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
Points of conflict between the principles of general relativity and quantum theory are highlighted. I argue that the current language of QFT is inadequete to deal with gravity and review attempts to identify some of the features which are…
This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two…