In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states. A multi-particle state is said to be free (non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation below. Asymptotically free then means that the state has this appearance in either the distant past or the distant future. While the S-matrix may be defined for any background (spacetime) that is asymptotically solvable and has no event horizons, it has a simple form in the case of the Minkowski space. In this special case, the Hilbert space is a space of irreducible unitary representations of the inhomogeneous Lorentz group (the Poincaré group); the S-matrix is the evolution operator between (the distant past), and (the distant future). It is defined only in the limit of zero energy density (or infinite particle separation distance). It can be shown that if a quantum field theory in Minkowski space has a mass gap, the state in the asymptotic past and in the asymptotic future are both described by Fock spaces. (Wikipedia).
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
This video introduces the identity matrix and illustrates the properties of the identity matrix. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
Matrix Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist Algebra
This is the second video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with multiplying two matrices. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Matrix Addition, Subtraction, and Scalar Multiplication
This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
Introduction to Matrix Transformations
This video defines a matrix transformation, linear transformation and provides example on how to find images of a transformation.
From playlist Matrix (Linear) Transformations
Linear Algebra 23b: How to Determine the Matrices Q and S in the Polar Decomposition
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Become a Linear Algebra Pro by trying out Brilliant! =D https://brilliant.org/FlammableMaths Complex Numbers but Different Playlist: https://www.youtube.com/playlist?list=PLN2B6ZNu6xmcg3R4wfUlIxtfgtr-2GYAm Today we are going to take the factorial of a matrix and see what we are going to g
From playlist Linear Algebra
Diagonalization of matrices | Lecture 35 | Matrix Algebra for Engineers
How to diagonalize a matrix using eigenvalues and eigenvectors. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub
From playlist Matrix Algebra for Engineers
Linear Algebra 23e: Reversing the Multiplicative Terms in the Polar Decomposition
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
22. Diagonalization and Powers of A
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 22. Diagonalization and Powers of A License: Creative Commons BY-NC-SA More information at htt
From playlist MIT 18.06 Linear Algebra, Spring 2005
Diagonalization of matrices example | Lecture 36 | Matrix Algebra for Engineers
An example of matrix diagonalization. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Matrix Algebra for Engineers
57 - Compatability with operations on matrix representations
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Landau-Ginzburg - Seminar 6 - Matrix factorisations and geometry
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this seminar Rohan Hitchcock defines matrix factorisations and gives some examples, and explains how to extract an algebraic set from a matrix factorisation.
From playlist Metauni
Motivation for the definition of matrix multiplication. Alternative ways of thinking about matrix multiplication.
From playlist Linear Algebra Done Right
Powers of a matrix | Lecture 37 | Matrix Algebra for Engineers
How to compute a matrix to a power by diagonalizing the matrix. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?
From playlist Matrix Algebra for Engineers
Understanding Matrices and Matrix Notation
In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start
From playlist Mathematics (All Of It)