Pseudoscalar (mathematics) | Wikipedia audio article
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00:00:11 1 Pseudoscalars in physics
00:00:22 1.1 Example pseudoscalars
00:00:34 2 Pseudoscalars in geometric algebra
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SUMMARY
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In physics, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not.
Any scalar product between a pseudovector and an ordinary vector is a pseudoscalar. The prototypical example of a pseudoscalar is the scalar triple product, which can be written as the scalar product between one of the vectors in the triple product and the cross product between the two other vectors, where the latter is a pseudovector. A pseudoscalar, when multiplied by an ordinary vector, becomes a pseudovector (axial vector); a similar construction creates the pseudotensor.
Mathematically, a pseudoscalar is an element of the top exterior power of a vector space, or the top power of a Clifford algebra; see pseudoscalar (Clifford algebra). More generally, it is an element of the canonical bundle of a differentiable manifold.