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algebra of physical space
In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra ''C''ℓ3 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 ''C''ℓ3 has a faithful representation, generated by Pauli matrices, on the spin representation C2; further, ''C''ℓ3 is isomorphic to the ''even'' subalgebra of the 3+1 Clifford algebra, ''C''ℓ.
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 ''C''ℓ1,3(R) of the four-dimensional Minkowski spacetime.
==Special relativity==
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