Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Magnetic Scattering: Pairwise Little Group and Pairwise Helicity

Description

This lecture delves into the properties of magnetic scattering, focusing on the pairwise little group and pairwise helicity. It covers the construction of the magnetic S-matrix for 2→2 electric-magnetic scattering, helicity flip, and monopole harmonics. The instructor discusses the multi-particle representations of the Poincare group, emphasizing the importance of pairwise spinor-helicity variables. The lecture explores the implications of the pairwise little group on angular momentum and the S-matrix transformation. It concludes with a detailed analysis of the general 3-point S-matrix and the partial wave expansion for magnetic cases, including the massless limit and higher partial waves.

Official source

Related concepts (32)

Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

Angular momentum

In physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.

Matrix exponential

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where is defined to be the identity matrix with the same dimensions as .

Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.

Matrix multiplication

In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.

Related lectures (31)

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Asymptotic States and S-matrix: Operators

Explores asymptotic states, S-matrix, and operators in quantum field theory, emphasizing the role of discrete symmetries and complete sets of states.

Plasma Collisions: Coulomb Force

Analyzes Coulomb collisions between charged particles and the conservation of energy, momentum, and angular momentum.

Asymptotic States and S-matrix

Covers the concept of asymptotic states and S-matrix in quantum field theory, focusing on the evolution of wave packets and the scattering states.

Electron-positron annihilation