Related papers: The Relation Between Classical and Quantum Mechani…
Measurement theory in classical mechanics is investigated in the formulation of classical mechanics by Koopman and von Neumann (KvN), using Hilbert space. It is shown that the classical and the quantum measurements give different "relative…
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical…
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
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,…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
The connection between topology and quantum mechanics is one of the cornerstones of modern physics. Several examples of current interest like the Aharonov-Bohm effect in quantum mechanics, monopoles and instantons in quantum field theory,…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and therefore,…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…