Related papers: Geometrization of Quantum Mechanics
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
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…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. In this letter we present a general method based on quantum tomography for…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
Approximation methods for calculating individual particle/ field motions in spacetime at the quantum level of accuracy (a key feature of the Bohm Picture of Quantum Mechanics (BP)), are studied. Modern textbook presentations of Quantum…