ABSTRACT
Space–time structure in special relativity is determined by the set of general principles: Space and time are homogeneous; Space is isotropic; and In all inertial reference systems the speed of light has the same value c. From the mathematical point of view, these principles mean that the space–time coordinates of two arbitrary inertial reference systems are related by a linear non-homogeneous transformation leaving the metric invariant. This chapter focuses on constructing a universal covering group of the Poincare group. Invariant tensors of the Lorentz group are useful for lowering, raising or covariant contraction of indices. The different invariant tensors include: the Minkowski metric and its inverse, the spinor metrics and their inverse, and the Levi–Civita totally antisymmetric tensor. The Lorentz group and its universal covering group are locally isomorphic. In quantum field theory, Poincare invariance means that any Poincare transformation induces a unitary transformation acting in a Hilbert space of particle states.
