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Geometric Algebra for Physicists Anthony Lasenby, Chris Doran
Publisher: Cambridge University Press

The case of most interest in physics is V=\mathbf R^4, (\cdot,\cdot) the Minkowski inner product of signature (3,1). While a was a full-time physics and maths student, i seldom, if ever, thought of proving anything using a diagram, or any kind of non-algebraic method, for that matter. Quantization in physics (Snyder studied an interesting noncommutative space in the late 1940s). Analytic geometry could be moved into Algebra II – and there would be time as the “review” of solving systems wouldn't be needed as there wouldn't be the year off. So, I'm looking for some valid reasons why this This connection is, on the one hand, natural (a 4-year old can tell a circle from an oval from a square) and, on the other hand, deep (geometry is the indispensible apparatus of classical mechanics and other physics). Those with a graduate education in physics are already familiar with the Geometric Algebra (GA) in that it is equivalent to the Gamma matrices used throughout quantum field theory. The idea of noncommutative geometry is to encode everything about the geometry of a space algebraically and then allow all commutative function algebras to be generalized to possibly non-commutative algebras. More generally, noncommutative geometry means There are many sources of noncommutative spaces, e.g. The theory of Clifford algebras for real vector spaces V is rather complicated. Piazzese [Clifford Algebras and their Applications in Mathematical Physics, F.