In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cℓ3 of the three-dimensional Euclidean space as a model for (3+1)-dimensional space-time, representing a point in space-time via a paravector (3-dimensional vector plus a 1-dimensional scalar).
The Clifford algebra Cℓ3 has a faithful representation, generated by Pauli matrices, on the spin representation C2; further, Cℓ3 is isomorphic to the even subalgebra of the 3+1 Clifford algebra, Cℓ0
3,1.
APS can be used to construct a compact, unified and geometrical formalism for both classical and quantum mechanics.
APS should not be confused with spacetime algebra (STA), which concerns the Clifford algebra Cℓ1,3(R) of the four dimensional Minkowski spacetime.
Read more about Algebra Of Physical Space: Special Relativity, Classical Electrodynamics, Relativistic Quantum Mechanics, Classical Spinor
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