Related papers: Classical and Quantum Mechanics via Lie algebras
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is…
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…
When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, and the differences between classical and quantum information, with emphasis in their manipulation through…
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality.…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are rough images of the fundamental {\bf…
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…
This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…