Algebra of physical space

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In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl_3,0(R) of the three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a paravector (3-dimensional vector plus a 1-dimensional scalar).

The Clifford algebra Cl_3,0(R) has a faithful representation, generated by Pauli matrices, on the spin representation C²; further, Cl_3,0(R) is isomorphic to the even subalgebra Cl^[0]
_3,1(R) of the Clifford algebra Cl_3,1(R).

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 Cl_1,3(R) of the four-dimensional Minkowski spacetime.