Related papers: Matrix Revolutions, The Origin of Quantum Variable…
This text consists on a series of introductory lectures on cosmology for mathematicians and physicists who are not specialized on the subject.
This paper explores the historical development of the theory of quantum mechanics between 1900 and 1927 by chronological examination of the foundational papers and ideas. Beginning with Planck's introduction of energy quantisation in…
Quantum Mechanics at Planck scale is considered as a deformation of the conventional Quantum Mechanics. Similar to the earlier works of the author, the main object of deformation is the density matrix. On this basis a notion of the entropy…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These equations, originating in the physics of 2-dimensional…
Quantum computing is a fascinating interdisciplinary research field that promises to revolutionize computing by efficiently solving previously intractable problems. Recent years have seen tremendous progress on both the experimental…
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation $[\hat P,\hat M]=1$. In ordinary quantum mechanics $\hat P$ is the derivative and $\hat M$ the coordinate operator. Here we shall realize $\hat P$ as…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
The purpose of this work is to retrace the steps that were made by scientists of XX century, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and…
In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal obserlvable length), as a fundamental part of the quantization process of the electrodynamical…
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date. 0. Canned…
It is discussed an opportunity to introduce new class of quantum algorithms based on possibility to express amplitude of transition between two states of quantum system as sum of some function along all possible classical paths. Continuous…
Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its…
The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It…
After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the…