Related papers: A lecture on the classical KAM theorem
The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it…
This is a series of lectures on M Theory for cosmologists. After summarizing some of the main properties of M Theory and its dualities I show how it can be used to address various fundamental and phenomenological issues in cosmology.
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
The aim of this review is to give a pedagogical introduction to our recently proposed ab initio theory of quantum transport.
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
A modest aim of this pedagogical presentation is to analyze, critically, certain fundamental physical concepts to illustrate the physical principles behind the special theory of relativity and, hence, to also illustrate the limitations of…
The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…
This is the second of a series of popular lectures on quantum chromodynamics. The first (introductory) lecture can be found here: https://scfh.ru/blogs/O_fizike_i_fizikah/polet-nad-kvantovoy-khromodinamikoy/ The lecture deals with the one…
For a century, quantum theorists have been reading the mathematical entrails of quantum mechanics (QM) to divine the nature of quantum reality. But to little avail. In this paper a different approach is taken, namely to identify and explain…
We provide a simple proof of Kamp's theorem.
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.
The aim of this paper is to introduce a mathematical logic based approach investigating why-type questions in physics.
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required…
The aim of these lectures is to provide (experimental particle physics Ph.D.) students with an introduction to some of the core concepts and methods of QCD that are relevant in an LHC context.