Art of spin decomposition

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.

5 pages, no figure; published in Phys.Rev.D (Rapid Communications)

References in corpus (11)

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Cited by in corpus (9)

• Notes on the orbital angular momentum of quarks in the nucleon
• Is gauge-invariant complete decomposition of the nucleon spin possible ?
• Wilson lines and orbital angular momentum
• Geometrical approach to the proton spin decomposition
• Angular momentum sum rule for spin one hadronic systems
• More on the relation between the two physically inequivalent decompositions of the nucleon spin and momentum
• Gauge-covariant canonical formalism revisited with application to the proton spin decomposition
• Are there infinitely many decompositions of the nucleon spin ?
• Gauge dependence of spontaneous radiation spectrum in a time-dependent relativistic non-perturbative Coulomb field