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

Lecture

Asymptotic States and S-matrix

In course

PHYS-432: Quantum field theory II

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics. ...

Description

This lecture covers the concept of asymptotic states and S-matrix in quantum field theory, focusing on the evolution of wave packets and the scattering states. The instructor explains the importance of discrete symmetries and the role of S-matrix in potential scattering. The lecture delves into the formalism of S-matrix elements and their relation to the Lippmann-Schwinger equation, emphasizing the unitarity of the S-matrix. Additionally, the lecture discusses the measurement in quantum mechanics, spin preparation, and the possibilities of spin states. The content also includes the application of the S-matrix in understanding the interaction amplitudes and the unitarity of the theory.

Instructors (2)

Riccardo Rattazzi

Riccardo Rattazzi was born in Novara (Italy) in 1964. He studied physics at the University of Pisa, where he received the Laurea cum laude in 1987, and at the Scuola Normale Superiore where he received the Diploma in Scienze and carried out graduate research in theoretical physics. After having been a post-doctoral research associate at the Lawrence Berkeley Laboratory, at Rutgers University and at CERN, in 1998 Riccardo obtained a permanent research position at the Istituto Nazionale di Fisica Nucleare in Pisa. From 2001 to 2006 he was a staff member at the Theory Division of CERN. In 2006 he was appointed professor of physics at EPFL.

Brando Bellazzini

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related concepts (32)

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.

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.

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 decomposition

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.

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 (48)

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.

Asymptotic States and S-matrix

Explores asymptotic states, S-matrix, Lippmann-Schwinger equation, and energy robustness in quantum field theory.

Quantum Fluids: Cross Section & Lifetime

Covers the concepts of cross section and lifetime in quantum fluids, focusing on transition and differential probabilities.

Quantum Field Theory II: Cross Section & Lifetime

Covers cross section, lifetime, quantum fluid, asymptotic states, discrete symmetries, and normal ordering in quantum field theory.

Scattering Theory Overview