Representation theory

Nonlinear realization

In mathematical physics, nonlinear realization of a Lie group G possessing a Cartan subgroup H is a particular induced representation of G. In fact, it is a representation of a Lie algebra of G in a neighborhood of its origin.A nonlinear realization, when restricted to the subgroup H reduces to a linear representation. A nonlinear realization technique is part and parcel of many field theories with spontaneous symmetry breaking, e.g., chiral models, chiral symmetry breaking, Goldstone boson theory, classical Higgs field theory, gauge gravitation theory and supergravity. Let G be a Lie group and H its Cartan subgroup which admits a linear representation in a vector space V. A Liealgebra of G splits into the sum of the Cartan subalgebra of H and its supplement , such that (In physics, for instance, amount to vector generators and to axial ones.) There exists an open neighborhood U of the unit of G suchthat any element is uniquely brought into the form Let be an open neighborhood of the unit of G such that, and let be an open neighborhood of theH-invariant center of the quotient G/H which consists of elements Then there is a local section of over . With this local section, one can define the induced representation, called the nonlinear realization, of elements on given by the expressions The corresponding nonlinear realization of a Lie algebra of G takes the following form. Let , be the bases for and , respectively, together with the commutation relations Then a desired nonlinear realization of in reads , up to the second order in . In physical models, the coefficients are treated as Goldstone fields. Similarly, nonlinear realizations of Lie superalgebras are considered. (Wikipedia).

Video thumbnail

C52 Introduction to nonlinear DEs

A first look at nonlinear differential equations. In this first video examples are shown of equations that still have explicit solutions.

From playlist Differential Equations

Video thumbnail

Linearising nonlinear derivatives

A simple trick to linearise derivatives

From playlist Linearisation

Video thumbnail

What is a linear equation

👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

Video thumbnail

Learn step by step how to find the inverse of an equation, then determine if a function or not

👉 Learn how to find the inverse of a linear function. A linear function is a function whose highest exponent in the variable(s) is 1. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of a function is that whe

From playlist Find the Inverse of a Function

Video thumbnail

Linear versus Nonlinear Differential Equations

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Linear versus Nonlinear Differential Equations

From playlist Differential Equations

Video thumbnail

Summary for graph an equation in Standard form

👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

Video thumbnail

What is exactly an equation multiplier

👉 Learn all about the processes and definitions for solving linear equations. You will gain a better understanding about the vocabulary and steps used to solve liner equations such as how to isolate an equation and apply inverse operation using the property of equality. We will work step b

From playlist Solve Linear Equations | Learn About

Video thumbnail

Jin-Peng Liu - Efficient quantum algorithms for nonlinear ODEs and PDEs - IPAM at UCLA

Recorded 27 January 2022. Jin-Peng Liu of the University of Maryland presents "Efficient quantum algorithms for nonlinear ODEs and PDEs" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Nonlinear dynamics play a prominent role in many domains and are notoriously difficult to

From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022

Video thumbnail

Parity-Time Symmetric Oscillator with Nonlinear Dissipation by Amarendra Kumar Sharma

Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys

From playlist Non-Hermitian Physics - PHHQP XVIII

Video thumbnail

Some thoughts on plasma-based acceleration (PBA)...(Lecture - 01) by Warren Mori

06 March 2017 to 17 March 2017 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Particle accelerators have been instrumental in unraveling some of the deep questions related to matter at the fundamental level, the latest being discovery of the Higgs Boson. The conventional accelerators, how

From playlist Laser Plasma Accelerator

Video thumbnail

SN Partial Differential Equations and Applications Webinar - Arnulf Jentzen

Join Arnulf Jentzen of University of Münster as he proves that suitable deep neural network approximations do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs and thereby proves, for the first time, that a general semilinear parabolic

From playlist Talks of Mathematics Münster's reseachers

Video thumbnail

The Power of Nonlinearities - A. Marandi - 11/11/2020

Earnest C. Watson Lecture by Professor Marandi, "The Power of Nonlinearities: Unlocking Opportunities for Sensing and Computing with Light." As the information age evolves, we are faced with new challenges in how to capture and process information. Nonlinearity, which leads to functions

From playlist Caltech Watson Lecture Series

Video thumbnail

Data-Driven Control: Linear System Identification

Overview lecture on linear system identification and model reduction. This lecture discusses how we obtain reduced-order models from data that optimally capture input--output dynamics. https://www.eigensteve.com/

From playlist Data-Driven Control with Machine Learning

Video thumbnail

Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control

This video illustrates the use of the Koopman operator to simulate and control a nonlinear dynamical system using a linear dynamical system on an observable subspace. From the Paper: Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for contro

From playlist Research Abstracts from Brunton Lab

Video thumbnail

Dynamics of Thin Liquid Films in Zero Gravity: Stabilization of Destabilization

For the latest information, please visit: http://www.wolfram.com Speaker: Aneet Dharmavaram Narendranath Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and more.

From playlist Wolfram Technology Conference 2016

Video thumbnail

Lecture 03 -The Linear Model I

The Linear Model I - Linear classification and linear regression. Extending linear models through nonlinear transforms. Lecture 3 of 18 of Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa. View course materials in iTunes U Course App - https://itunes.apple.com/us/c

From playlist Machine Learning Course - CS 156

Video thumbnail

Stiefel Liquids: Possibly Non-Lagrangian Critical Spin Liquids by Yin-Chen He

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

Video thumbnail

What are parallel lines

👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

Related pages

Lie group | Chiral symmetry breaking | Induced representation | Lie superalgebra | Cartan subgroup | Higgs field (classical) | Spontaneous symmetry breaking | Cartan subalgebra | Lie algebra | Supergravity