Noether’s theorem and its complement in multi-particle systems

Abstract

Noether’s theorem has gained outstanding importance in theoretical particle physics, because it leads to basic conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem, but unnoticed so far, is a complementary law, which requires the (virtual) exchange of momentum between the particles of an isolated multi-particle system. This exchange of momentum determines an interaction. For a two-particle system defined by an irreducible representation of the Poincaré group, this interaction is identified as the electromagnetic interaction. This sheds new light on the particle interactions described by the Standard Model. It resolves long-standing questions about the value of the electromagnetic coupling constant, and about divergent integrals in quantum electrodynamics.