Related papers: Quantum Mechanics on Manifolds
Despite the impressive amount of literature on the foundations of quantum mechanics, the relevance of symmetry in interpretation is not properly acknowledged. In fact, although it is usually said that quantum mechanics is invariant under…
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
Let U be the quantum group associated to a symmetrizable generalized Cartan matrix. We give a realization of U from the category of the representations of certain product valued quiver.
Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems…
Given an equivalence relation ~ on a set U, there are two abstract notions of an element of the quotient set U/~. The #1 abstract notion is a set S=[u] of equivalent elements of U (an equivalence class); the #2 notion is an abstract entity…
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the…
Quantum Mechanics, almost 80 years after its arrival, is a well established and experimentally not falsified theory. It has predicted and explained a whole series of natural phenomena of a very delicate nature. But its interpretation has…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
After recalling briefly some basic properties of the quantum group $GL_q(2)$, we study the quantum sphere $S_q^2$, quantum projective space $CP_q(N)$ and quantum Grassmannians as examples of complex (K\"{a}hler) quantum manifolds. The…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
We propose a formulation of quantum mechanics in three dimensions with spherical symmetry for a finite level system whose dynamics is not governed by a differential equation of motion. The wavefunction is written as an infinite sum in a…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…