Lorentz Group in Feynman's World

TL;DR

This paper demonstrates how the Lorentz group provides a mathematical foundation for Feynman's parton model, linking it to relativistic symmetries and extending it to particles with space-time extensions.

Contribution

It introduces a Lorentz-covariant framework for the parton model using the Lorentz group and harmonic oscillators, connecting Feynman's ideas to relativistic symmetry principles.

Findings

Lorentz group underpins the parton model.

Massless and massive particles' symmetries are related via the little group.

Oscillator formalism models relativistic extended hadrons.

Abstract

R. P. Feynman was quite fond of inventing new physics. It is shown that some of his physical ideas can be supported by the mathematical instruments available from the Lorentz group. As a consequence, it is possible to construct a Lorentz-covariant picture of the parton model. It is shown first how the Lorentz group can be used for studying the internal space-time symmetries of relativistic particles. These symmetries are dictated by Wigner's little groups, whose transformations leave the energy-momentum four-vector of a given particle invariant. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted that the E(2)-like symmetry of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like little group for massive particles. It is shown that the formalism can be extended to cover relativistic particles with space-time extensions, such as heavy ions and hadrons in the quark model. It is possible to construct representations of the little group using harmonic oscillators, which Feynman et al. used for studying relativistic extended hadrons. This oscillator formalism allows us to show that Feynman's parton model is a Lorentz-boosted quark model. The formalism also allows us to explain in detail Feynman's rest of the universe which is contained in his parton picture.