# Mathematical methods

# Mathematical methods

This chapter provides a resume of the mathematical tools that are used to explain and understand the Standard Model of particle physics and the experimental data that support it. Various aspects of symmetry in physics are covered, in particular three-dimensional rotational symmetry and its associated quantum-mechanical formalism and Lorentz covariance. The invariant variables of two-body interactions, namely *s* (centre-of-mass energy squared) and *t* (4-momentum transfer squared), are defined and examples of their use are given. The concepts of cross section and phase space are introduced with examples from two- and three-body final states. The importance of graphical tools is outlined with an explanation and example of a Dalitz plot. The Breit–Wigner formula for an unstable state is explained. The last sections of the chapter cover group theory, in particular the Lie groups U(*n*) and SU(*n*).

*Keywords:*
rotational symmetry, Lorentz covariance, cross section, phase space, Breit–Wigner, Lie group

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