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arXiv · 1105.6304

Art of spin decomposition

Xiang-Song Chen·Wei-Min Sun·Fan Wang·T. Goldman
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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.

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Xiang-Song Chen, Wei-Min Sun, Fan Wang, T. Goldman. 2011-05-31. Art of spin decomposition. https://doi.org/10.1103/physrevd.83.071901

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