In the approximation of classical relativistic theory the creation of an electron pair (electron A, positron B) might be represented by the start of two world lines from the point of creation, 1. The world lines of the positron will then continue until it annihilates another electron, C, at a world point 2.

The Gordon identity, introduced in Section 10.19, allows us to decompose the point-like QED current into two parts

Just in the same way as the scattering of 𝛼 particles on nuclei has been fundamental to develop the atomic model, our understanding about the internal structure of the proton has enormously benefited from scattering studies using electrons as probes. In this kind of experiment, we bombard target protons with electrons of generally fixed energy and study the scattered electron properties (its energy and angle) to infer the structure properties of the proton.

Historically, the behavior of light (or more generally electromagnetic radiation) represented a failure of classical mechanics known at the beginning of the twentieth century. On the one hand, the phenomena of interference and diffraction could be explained only on the basis of a wave theory. On the other hand, phenomena such as photoelectric emission and scattering by free electrons showed that light is composed of small particles.

The electroweak theory is a very powerful theory which can be used to compute many processes. The gauge sector is fully determined by only three independent parameters which completely fix the gauge boson masses and their coupling to fermions.

In principle and with the help of Feynman diagrams, it could be possible to compute any reaction at any desired precision. In practice, calculations become increasingly complex endeavors as the precision increases, with the number of diagrams to compute growing rapidly with the increasing order under consideration. The tree-level calculation corresponds to the lowest possible order. The first, second, … order radiative corrections are added when adding additional vertices, with either external legs and/or internal lines or loops.

The general scheme for producing modern high-energy neutrinos follows from the one pioneered in the BNL-Columbia experiment (see Sections 21.10 and 21.11). At high-energy accelerators (typically with primary protons of tens of giga-electronvolts), neutrinos produced in decays of secondaries have some interesting properties.

In the electroweak theory, we need to consider the couplings of the leptons and quarks to three different physical gauge bosons: the photon, the 𝑊±, and the 𝑍0.

If a physical system behaves the same, regardless of how it is oriented in space, the physical laws that govern it are rotationally symmetric; from this symmetry, Noether’s theorem shows the angular momentum of the system must be conserved. The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. Rather, the symmetry of the physical laws governing the system is responsible for the conservation law. As another example, if a physical experiment has the same outcome at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether’s theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively.

Electron–positron colliders and their associated high-performance detectors have provided excellent environments to test QED at increasingly higher center-of-mass energies. Table 3.1 presented a comprehensive list of 𝑒+𝑒− colliders. Each new generation of collider, with their corresponding experiments, has provided excellent environments to study the properties of QED at high energy.