The relativistic center of mass in field theory with spin

TL;DR

This paper explores the relativistic center of mass in field theory with spin, linking it to nucleon spin studies, asymmetric energy-momentum tensors, and light-front formalism, revealing observer-dependent effects and their impact on parton distributions.

Contribution

It generalizes the relativistic center of mass concept to asymmetric energy-momentum tensors and connects it with light-front formalism, explaining observer-dependent effects in nucleon spin structure.

Findings

Relativistic quantum effects cause the canonical reference point to depend on the observer.

The p-wave in Dirac solutions arises from relativistic effects.

Observer dependence explains shifts in parton distributions.

Abstract

In order to unravel the origin of the nucleon spin, one has to study in detail the question of orbital angular momentum, and in particular the reference point about which it is defined. With this in mind, we review the concept of relativistic center of mass, generalize the discussion to the case of asymmetric energy-momentum tensors, and establish the link with the light-front formalism. We find that the $p$-wave in the Dirac plane-wave solutions arises from a relativistic quantum-mechanical effect which forces the canonical reference point to depend on the observer. This explains why longitudinal spin is much simpler to study than transverse spin. It is also the reason behind the observation of induced shifts and distortions in the parton distributions defined within the light-front formalism.