Art of spin decomposition

TL;DR

This paper explores spin decomposition in interacting systems, proposing gauge-dependent and gauge-invariant methods to identify conserved angular momentum components, clarifying nucleon spin decomposition.

Contribution

It introduces a gauge-invariant approach to spin decomposition, providing clarity on the most relevant method for nucleon spin analysis.

Findings

Constructed a gauge-invariant spin operator with conserved properties.

Clarified the relation between gauge choices and angular momentum decomposition.

Provided insights into the most pertinent decomposition method for nucleon spin.

Abstract

We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular momentum eigenstates. We split, from the total angular momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.