Pseudoscalar

In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion^[1]^[2] while a true scalar does not.

A pseudoscalar, when multiplied by an ordinary vector, becomes a pseudovector (or axial vector); a similar construction creates the pseudotensor. A pseudoscalar also results from any scalar product between a pseudovector and an ordinary vector. 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.

^ Zee, Anthony (2010). "II. Dirac and the Spinor II.1 The Dirac Equation § Parity". Quantum field theory in a nutshell (2nd ed.). Princeton University Press. p. 98. ISBN 978-0-691-14034-6.
^ Weinberg, Steven (1995). "5.5 Causal Dirac Fields §5.5.57". The quantum theory of fields. Vol. 1: Foundations. Cambridge University Press. p. 228. ISBN 9780521550017.

[1] Zee, Anthony (2010). "II. Dirac and the Spinor II.1 The Dirac Equation § Parity". Quantum field theory in a nutshell (2nd ed.). Princeton University Press. p. 98. ISBN 978-0-691-14034-6.

[2] Weinberg, Steven (1995). "5.5 Causal Dirac Fields §5.5.57". The quantum theory of fields. Vol. 1: Foundations. Cambridge University Press. p. 228. ISBN 9780521550017.

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