Related papers: Introduction to Quantum Mechanics and the Quantum-…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. Quantum mechanics constrains relationships between kinematic parameters and the coordinates describing the dynamics. Example quantum…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
Cirelli, Mani\`{a} and Pizzocchero generalized quantum mechanics by K\"{a}hler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative…
We briefly report our application of a version of noncommutative geometry to the quantum Euclidean space $R^N_q$, for any $N \ge 3$; this space is covariant under the action of the quantum group $SO_q(N)$, and two covariant differential…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
These lecture notes cover the important developments in histories approach to quantum mechanics with overall content and emphasis somewhat different from other reviews and books on the subject.The idea of Houtappel, Van Dam and Wigner of…
Using extended Schwinger's quantization approach quantum mechanics on a Riemannian manifold $M$ with a given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined unequivocally…
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 describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
The canonical commutation relation, $[Q,P] = i\hbar$, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of $P$ & $Q$ as observables has always relied on the analogies that exist between the…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which 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…
Heisenberg's uncertainty relation means that one observer cannot know an exact position and velocity for another (finite mass) observer. By contrast, the Poincare transformation of classical special relativity assumes that one observer…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…