Axiomatic quantum field theory | Theorems in quantum mechanics
While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now commonly known as Haag’s theorem. Haag’s original proof relied on the specific form of then-common field theories, but subsequently generalized by a number of authors, notably Hall & Wightman, who concluded that no single, universal Hilbert space representation can describe both free and interacting fields. A generalization due to Reed & Simon shows that applies to free neutral scalar fields of different masses, which implies that the interaction picture is always inconsistent, even in the case of a free field. (Wikipedia).
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
Hausdorff Example 3: Function Spaces
Point Set Topology: For a third example, we consider function spaces. We begin with the space of continuous functions on [0,1]. As a metric space, this example is Hausdorff, but not complete. We consider Cauchy sequences and a possible completion.
From playlist Point Set Topology
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Minimal time for the bilinear control of Schrodinger (...) - K. Beauchard - Workshop 2 - CEB T2 2018
Karine Beauchard (ENS Rennes) / 05.06.2018 Minimal time for the bilinear control of Schrodinger equations We consider a quantum particle in a potential V(x) and a time dependent electric field E(t), which is the control. Boscain, Caponigro, Chambrion and Sigalotti proved in [2] that, und
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
Hausdorff Example 1: Cofinite Topology
Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.
From playlist Point Set Topology
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
This lecture is part of an online graduate course on Lie groups. We show the existence of a left-invariant measure (Haar measure) on a Lie group. and work out several explicit examples of it. Correction: At 21:40 There is an exponent of -1 missing: the parametrization of the unitary gro
From playlist Lie groups
CEO Rob Shuter Vodafone Nederland deel 1
CEO Rob Shuter van Vodafone Nederland geeft een update over de storing via een videoboodschap
From playlist Vodafone brand 2012
Claire Voisin - Schiffer variations of hypersurfaces and the generic Torelli theorem - WAGON
The generic Torelli theorem for hypersurfaces of degree d and dimension n-1 was proved by Donagi in the 90's. It works under the assumption that d is at least 7 and d does not divide n+1, which in particular excludes the Calabi-Yau case in all dimensions. We prove that the generic Torelli
From playlist WAGON
What is the distance between two sets of points? | Hausdorff Distance
What is the distance between two sets of points is a non-trivial question that has applications all over the place, from bioinformatics and computer science to fractal geometry. In this video, I'll give a bit of motivation, introduce the delta expansion of a set and then give the distance
From playlist The New CHALKboard
Sinh-Gordon equation and application to the geometry of CMC surfaces - Laurent Hauswirth
Workshop on Mean Curvature and Regularity Topic: Sinh-Gordon equation and application to the geometry of CMC surfaces. Speaker: Laurent Hauswirth Affiliation: Université de Marne-la-Vallée Date: November 7, 2018 For more video please visit http://video.ias.edu
From playlist Workshop on Mean Curvature and Regularity
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - R.Gohm
Rolf Gohm (Aberystwyth) / 11.09.17 Title:Asymptotic Completeness and Controllability of Open Quantum Systems Abstract:Repeated interactions of an open quantum system with copies of another system can be interpreted as a quantum Markov process. The notion of asymptotic completeness from
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Henri Epstein - Archeological Remarks on Analyticity Properties in Momentum Space in QFT
I will describe the foundations of the program of studying the analyticity properties of the n-point functions in momentum space : the primitive domain of analyticity and methods to enlarge it. If time permits, some of the results for the 4-point function will be described. Henri Epstein
From playlist Les séminaires de l'IHES
Claude Lefèvre: Discrete Schur-constant models in inssurance
Abstract : This paper introduces a class of Schur-constant survival models, of dimension n, for arithmetic non-negative random variables. Such a model is defined through a univariate survival function that is shown to be n-monotone. Two general representations are obtained, by conditioning
From playlist Probability and Statistics
The Hague Where I was Born and Raised
I Lived my First 17 years in Den Haag
From playlist Walter Lewin is Alive and Well!
Very young Walter Lewin. How young?
Amandelstraat 61, Den Haag, The Netherlands.
From playlist Walter Lewin is Alive and Well!
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
Valkenboslaan 230, Den Haag - My mother lived there 60 years.
From playlist Walter Lewin is Alive and Well!