Axiomatic quantum field theory | Theorems in complex analysis | Several complex variables | Theorems in mathematical physics

Edge-of-the-wedge theorem

In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the analytic continuation of Wightman functions. The formulation and the first proof of the theorem were presented by Nikolay Bogoliubov at the International Conference on Theoretical Physics, Seattle, USA (September, 1956) and also published in the book Problems in the Theory of Dispersion Relations. Further proofs and generalizations of the theorem were given by R. Jost and H. Lehmann (1957), F. Dyson (1958), H. Epstein (1960), and by other researchers. (Wikipedia).

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Proof: The Angle Bisector Theorem

This video states and proves the angle bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com

From playlist Relationships with Triangles

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Angle-Angle Triangle Similarity Theorem: Dynamic Proof

Link: https://www.geogebra.org/m/Q8EYTUK2

From playlist Geometry: Dynamic Interactives!

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Proof: The Angle Bisector Theorem Converse

This video states and proves the angle bisector theorem converse. Complete Video List: http://www.mathispower4u.yolasite.com

From playlist Relationships with Triangles

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Inscribed Angle Theorem: Proof Without Words

Link: https://www.geogebra.org/m/PgjnhjJF

From playlist Geometry: Dynamic Interactives!

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Angle Bisector Theorem

I introduce the Angle Bisector Theorem and prove it, introduce the Converse of the Angle Bisector Theorem, and finish by working through two examples. EXAMPLES AT 0:20 9:40 15:19 Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to s

From playlist Geometry

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The Triangle Angle Bisector Theorem

This video states and proves the triangle angle bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com

From playlist Similarity

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Angle Side / Base-Angle Theorem - Two Column Proofs

This geometry video tutorial explains how to use the angle side theorem also known as the base-angle theorem in two column proofs. The angle side theorem states that if two sides of a triangle are congruent, the angles are congruent and vice versa. This theorem typically applies to an is

From playlist Geometry Video Playlist

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Determine the values of two angles that lie on a lie with a third angle

👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships

From playlist Angle Relationships From a Figure

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Lecture 16: Discrete Curvature I (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

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Combinatorial methods for PIT (and ranks of matrix spaces) - Roy Meshulam

Optimization, Complexity and Invariant Theory Topic: Combinatorial methods for PIT (and ranks of matrix spaces) Speaker: Roy Meshulam Affiliation: Technion Date: June 8. 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

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Henry Adams (8/30/21): Vietoris-Rips complexes of hypercube graphs

Questions about Vietoris-Rips complexes of hypercube graphs arise naturally from problems in genetic recombination, and also from Kunneth formulas for persistent homology with the sum metric. We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at small scale param

From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021

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Francis BROWN - Graph Complexes, Invariant Differential Forms and Feynman integrals

Kontsevich introduced the graph complex GC2 in 1993 and raised the problem of determining its cohomology. This problem is of renewed importance following the recent work of Chan-Galatius-Payne, who related it to the cohomology of the moduli spaces Mg of curves of genus g. It is known by Wi

From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

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KPZ line ensemble - Ivan Corwin

Ivan Corwin Clay Mathematics Institute, Columbia University and MIT December 4, 2013 We construct a KPZtKPZt line ensemble -- a natural number indexed collection of random continuous curves which satisfies a resampling invariance called the H-Brownian Gibbs property (with H(x)=exH(x)=ex) a

From playlist Mathematics

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Tony Bahri, Research talk - 10 February 2015

Tony Bahri (Rider University) - Research talk http://www.crm.sns.it/course/4350/ I shall describe geometric and algebraic approaches to the computation of the cohomology of polyhedral products arising from homotopy theory. A report on joint work with Martin Bendersky, Fred Cohen and Sam G

From playlist Algebraic topology, geometric and combinatorial group theory - 2015

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AlgTop15: Rational curvature of a polytope

We use our new normalization of angle called turn-angle, or "tangle" to define the curvature of a polygon P at a vertex A. This number is obtained by studying the opposite cone at the vertex A, whose faces are perpendicular to the edges of P meeting at A. A classical theorem of Harriot on

From playlist Algebraic Topology: a beginner's course - N J Wildberger

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Lecture 9: Discrete Exterior Calculus (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

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Causality and Entanglement in Holography - The Connected Wedge Theorem Revisited - Jonathan Sorce

IAS It from Qubit Workshop Workshop on Spacetime and Quantum Information Tuesday December 6, 2022 Wolfensohn Hall One puzzling aspect of holography is that it conjectures a duality between a physical theory with a single rigid causal structure (the non-gravitational "boundary theory") and

From playlist IAS It from Qubit Workshop - Workshop on Spacetime and Quantum December 6-7, 2022

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Henry Adams (10/11/17): Metric reconstruction via optimal transport

Given a sample of points X in a metric space M and a scale parameter r, the Vietoris-Rips simplicial complex VR(X;r) is a standard construction to attempt to recover M from X up to homotopy type. A deficiency of this approach is that VR(X;r) is not metrizable if it is not locally finite, a

From playlist AATRN 2017

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Triangle Inequality Theorem

This video states and investigates the triangle inequality theorem. Complete Video List: http://www.mathispower4u.yolasite.com

From playlist Relationships with Triangles

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