Geometric algebra | Clifford algebras

Spacetime algebra

In mathematical physics, spacetime algebra (STA) is a name for the Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4). According to David Hestenes, spacetime algebra can be particularly closely associated with the geometry of special relativity and relativistic spacetime. It is a vector space that allows not only vectors, but also bivectors (directed quantities associated with particular planes, such as areas, or rotations) or blades (quantities associated with particular hyper-volumes) to be combined, as well as rotated, reflected, or Lorentz boosted. It is also the natural parent algebra of spinors in special relativity. These properties allow many of the most important equations in physics to be expressed in particularly simple forms, and can be very helpful towards a more geometric understanding of their meanings. (Wikipedia).

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A Swift Introduction to Spacetime Algebra

This video is a fast-paced introduction to Spacetime Algebra (STA), which is the geometric algebra of Minkowski space. In it, we figure out what the problems are with the way introductory textbooks usually describe special relativity and how we can solve those problems by using spacetime

From playlist Miscellaneous Math

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What is spacetime?

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From playlist Science Unplugged: Special Relativity

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QED Prerequisites Geometric Algebra: Spacetime.

In this lesson we continue our reading of an excellent paper on Geometric Algebra and spacetime algebra. The paper can be found here: https://arxiv.org/abs/1411.5002 We will cover section 3.1 and begin section 3.2. This material includes our first expansion of the vector space of spacet

From playlist QED- Prerequisite Topics

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Norm and distance in Euclidean n-Space.

From playlist Linear Algebra

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13B Vectors in n Space

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From playlist Linear Algebra

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QED Prerequisites Geometric Algebra 5- Multivectors

In this lesson we introduce the idea of multivectors and emphasize the need to understand how to take the spacetime product of any two multivectors in the Spacetime Algebra. We demonstrate how this is done for the product between a vector and a bivector and we interpret the meaning of each

From playlist QED- Prerequisite Topics

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What is General Relativity? Lesson 5: The Catalogue of Spacetimes

What is General Relativity? Lesson 5: The Catalogue of Spacetimes - Minkowski Spacetime I invite you to download the Catalog of Spacetimes at : https://arxiv.org/abs/0904.4184 to use as a reference for the rest of the course.

From playlist What is General Relativity?

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From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

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Lorentz Transformations | Special Relativity Ch. 3

Go to http://brilliant.org/MinutePhysics for 20% off a premium subscription to Brilliant! Mark Rober's youtube channel: https://www.youtube.com/markrober The previous videos in this series: Chapter 1: Why Relativity is Hard https://www.youtube.com/watch?v=1rLWVZVWfdY& Chapter 2: Spacetim

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Christian Gérard - Introduction to field theory on curved spacetimes (Part 1)

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From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

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Christian Gérard - Introduction to field theory on curved spacetimes (Part 2)

The aim of these lectures is to give an introduction to quantum field theory on curved spacetimes, from the point of view of partial differential equations and microlocal analysis. I will concentrate on free fields and quasi-free states, and say very little on interacting fields or perturb

From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

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Christian Gérard - Introduction to field theory on curved spacetimes (Part 3)

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From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

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Colloquium MathAlp 2018 - Christian Gérard

Aspects de la théorie quantique des champs en espace-temps courbe La théorie quantique des champs est formulée d'habitude sur l'espace-temps plat de Minkowski. L'extension de ce cadre à des espaces-temps généraux permet de mettre en lumière de nouveaux phénomènes quantiques qui surviennen

From playlist Colloquiums MathAlp

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Special Relativity: 2 - Spacetime Diagrams

An introduction to spacetime diagrams which are a valuable tool used to understand special relativity. The second in a series on special and general relativity. Let us know what you think of these videos by filling out our short survey at http://tinyurl.com/astronomy-pulsar. Thank you!

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From playlist WSU Master Classes

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WSU: Special Relativity with Brian Greene

Physicist Brian Greene takes you on a visual, conceptual, and mathematical exploration of Einstein’s spectacular insights into space, time, and energy. In just 11.5 hours, using nothing more advanced than high school algebra, journey from Einstein’s earliest musings on the speed of light t

From playlist WSU Master Class

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Scattering Amplitudes and Clusterhedra in Kinematic Space (Lecture 1) by Nima Arkani Hamed

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From playlist Gravity as Spacetime Curvature

Related pages

Clifford algebra | Vector space | Gauge theory gravity | Zero divisor | Blade (geometry) | Dirac algebra | Bivector | Spinor | Dirac equation | Directional derivative | Pseudoscalar | Minkowski space | Rotation | Real number | Scalar (mathematics) | Geometric algebra | Einstein notation | Division algebra | Reflection (mathematics) | Pseudovector