Pseudoscalar

A pseudoscalar is a scalar quantity that changes its sign under reflections in space . A pseudoscalar therefore has parity  −1. ${\displaystyle {\vec {x}}\rightarrow -{\vec {x}}}$

A pseudoscalar object property is handedness : A right hand appears in the mirror as a left one.

Further examples

A pseudoscalar arises e.g. B. as a scalar product of a direction vector with a rotation vector , rotation vectors in turn as a cross product of two direction vectors - a total of a late product :

${\displaystyle {\vec {a}}\cdot \left({\vec {b}}\times {\vec {c}}\right)}$

A physical example is the magnetic flux through a surface. It is defined as the scalar product of the magnetic flux density , a rotation vector , with the normal vector of the surface.

The pion is a pseudoscalar particle. Under Lorentz transformations , its quantum mechanical wave function behaves like a scalar, but with negative parity.

The angular momentum is, as the cross product of momentum and position vector, a rotation vector with amount , axis and direction of rotation. The combination of the direction of rotation with a direction of movement along the axis results in helicity . The parity violation in β-decay is evident from the helicity of elementary particles .