Noether's Theorem and its Complement: A Gateway to Particle Interaction

TL;DR

This paper explores a complementary law to Noether's theorem that explains particle interactions, particularly electromagnetic interactions, providing new insights into the Standard Model and longstanding quantum electrodynamics issues.

Contribution

It introduces a complementary law to Noether's theorem that accounts for virtual momentum exchange, offering a novel perspective on particle interactions and the electromagnetic coupling constant.

Findings

Identifies a complementary law to Noether's theorem related to momentum exchange.

Provides a new understanding of electromagnetic interactions in the Standard Model.

Addresses longstanding questions about the electromagnetic coupling constant and divergences in QED.

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 a closed multi-particle system. This exchange of momentum determines an interaction. For a two-particle system defined by an irreducible representation of the Poincare 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.