A path integral to quantize spin

H. B. Nielsen, Daniel Rohrlich

Research output: Contribution to journalArticlepeer-review

84 Scopus citations


We present a model for a classical spinning particle, characterized by spin magnitude, arbitrary but fixed, and continuously varying direction. A gauge freedom of the model reflects the choice of canonical coordinates in the phase space, which is spherical. We formulate the path integral for the model and find, unexpectedly, that the phase space must be punctured at the poles. It then follows that both the total spin and spin projection along any axis are quantized. The model has rotational invariance and yields the usual quantum mechanics of spin, including commutation relations, in a simple way.

Original languageEnglish
Pages (from-to)471-483
Number of pages13
JournalNuclear Physics B
Issue number3
StatePublished - 11 Apr 1988
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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