Fourvectors and Operators

Abstract

Abstract This chapter develops techniques that allow relativistically covariant calculations to be done in an elegant manner and introduces what are known as fourvectors. Fourvectors are analogous to the familiar vectors in three-dimensional Cartesian space (termed threevectors), except that, in additional to the three spatial components, fourvectors will have an additional zeroth component associated with time. This additional component allows us to deal with the fact that the Lorentz transformation of special relativity transforms time as well as spatial coordinates. The theory of fourvectors and operators is presented using an invariant notation. The concept of fourvectors and tensors is discussed in the simple context of special relativity, as well as the choice of metric, relativistic interval, space-time diagram, general fourvectors and construction of new fourvectors, covariant and contravariant components, general Lorentz transformations, transformation of components, examples of Lorentz transformations, gradient fourvector, manifest covariance, formal covariance, fourvector operators, fourvector dyadics, wedge products, and manifestly covariant form of Maxwell’s equations.