Representation theory of the Lorentz group

Representation theory: Introduction

This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irr

From playlist Representation theory

RT6. Representations on Function Spaces

Representation Theory: We note how to transfer a group action of a group G on a set X to a group action on F(X), the functions on X. Because F(X) is a vector space, we obtain a representation of the group, and we can apply previous techniques. In particular, the group acts on itself in

From playlist Representation Theory

Representation theory: Abelian groups

This lecture discusses the complex representations of finite abelian groups. We show that any group is iomorphic to its dual (the group of 1-dimensional representations, and isomorphic to its double dual in a canonical way (Pontryagin duality). We check the orthogonality relations for the

From playlist Representation theory

RT7.2. Finite Abelian Groups: Fourier Analysis

Representation Theory: With orthogonality of characters, we have an orthonormal basis of L^2(G). We note the basic philosophy behind the Fourier transform and apply it to the character basis. From this comes the definition of convolution, explored in 7.3. Course materials, including pro

From playlist Representation Theory

Representation Theory as Gauge Theory - David Ben-Zvi [2016]

Slides for this talk: https://drive.google.com/file/d/1FHl_tIOjp26vuULi0gkSgoIN7PMnKLXK/view?usp=sharing Notes for this talk: https://drive.google.com/file/d/1BpP2Sz_zHWa_SQLM6DC6T8b4v_VKZs1A/view?usp=sharing David Ben-Zvi (University of Texas, Austin) Title: Representation Theory as G

From playlist Number Theory

RT8.2. Finite Groups: Classification of Irreducibles

Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) usin

From playlist Representation Theory

RT1: Representation Theory Basics

Representation Theory: We present basic concepts about the representation theory of finite groups. Representations are defined, as are notions of invariant subspace, irreducibility and full reducibility. For a general finite group G, we suggest an analogue to the finite abelian case, whe

From playlist *** The Good Stuff ***

RT7.3. Finite Abelian Groups: Convolution

Representation Theory: We define convolution of two functions on L^2(G) and note general properties. Three themes: convolution as an analogue of matrix multiplication, convolution with character as an orthogonal projection on L^2(G), and using using convolution to project onto irreduci

From playlist Representation Theory

Representation theory: Frobenius groups

We recall the definition of a Frobenius group as a transitive permutation group such that any element fixing two points is the identity. Then we prove Frobenius's theorem that the identity together with the elements fixing no points is a normal subgroup. The proof uses induced representati

From playlist Representation theory

Sidney Coleman lecture 18

From playlist Full course: Quantum Field Theory by Sidney Coleman (1975) [Havard Physics 253]

Sidney Coleman lecture 19

From playlist Full course: Quantum Field Theory by Sidney Coleman (1975) [Havard Physics 253]

Introduction to Conformal Field Theory by Pedro Liendo

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography

Sidney Coleman lecture 20

From playlist Full course: Quantum Field Theory by Sidney Coleman (1975) [Havard Physics 253]

Introduction to Amplitudes (Lecture 1) by Marcus Spradlin

PROGRAM RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onlin

From playlist Recent Developments in S-matrix Theory (Online)

Supersymmetry and Superspace, Part 1 - Jon Bagger

Supersymmetry and Superspace, Part 1 Jon Bagger Johns Hopkins University July 19, 2010

From playlist PiTP 2010

Seiberg-Witten Theory, Part 1 - Edward Witten

Seiberg-Witten Theory, Part 1 Edward Witten Institute for Advanced Study July 19, 2010

From playlist PiTP 2010

Brian HENNING - Free field states and conformal bases

From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”

Sidney Coleman (Harvard) - Quantum Field Theory lecture 01 [1975]

Notes for this course: http://arxiv.org/abs/1110.5013 Physics 253: Quantum Field Theory Lectures by Sidney R. Coleman Recorded in 1975-1976. Full Playlist available here: https://www.youtube.com/playlist?list=PLhsb6tmzSpiwrZuDMyweABm7FShZu3YUv The videos shown here were transferred to D

From playlist Full course: Quantum Field Theory by Sidney Coleman (1975) [Havard Physics 253]

Representation theory: Orthogonality relations

This lecture is about the orthogonality relations of the character table of complex representations of a finite group. We show that these representations are unitary and deduce that they are all sums of irreducible representations. We then prove Schur's lemma describing the dimension of t

From playlist Representation theory

Lecture 02 | From Particles to Fields

In this lecture, I introduce states describing any number of particles and define operators acting on these states. I argue that causality requires that the theory be written in terms of "observables," local Hermitian operators that commute at spacelike positions. This leads us to a theory

From playlist UC Davis: Brief Overview of Relativistic Quantum Field Theory