The Källén function, also known as triangle function, is a polynomial function in three variables, which appears in geometry and particle physics. In the latter field it is usually denoted by the symbol . It is named after the theoretical physicist Gunnar Källén, who introduced it as a short-hand in his textbook Elementary Particle Physics.[1]
Definition
The function is given by a quadratic polynomial in three variables
Applications
In geometry the function describes the area of a triangle with side lengths :
The function appears naturally in the Kinematics of relativistic particles, e.g. when expressing the energy and momentum components in the center of mass frame by Mandelstam variables.[2]
Properties
The function is (obviously) symmetric in permutations of its arguments, as well as independent of a common sign flip of its arguments: