Abstract
The spin-statistics theorem is quite a remarkable one since it correlates two very distinct kinds of symmetries, namely spin symmetry, which is a property of single particles, and exchange symmetry, which is a property of sets of particles, and is trivial for single particles. The theorem is, of course, well-established within the framework of local relativistic field theory1, but for a number of reasons the time would seem to be ripe for placing it in a broader context. Among these reasons are the following:
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(a)
The theorem is now known to be valid for a variety of objects, notably extended objects such as solitons2 and strings3, which are not described by local relativistic field theory.
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(b)
With the advent of topological considerations in field theory it has been realized that the spin-statistics theorem has a topological basis4. Furthermore, it has been realized that it is only the first in a serties of topological properties, the next in the series being the existence of a Wess-Zumino (closed but not exact) 2-form5.
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(c)
There is a general feeling that, even within the context of local relativistic field theory, it should not be necessary to use the full machinery to establish the spin-statics correlation, but that it should follow directly from some key topological assumptions.
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© 1993 Springer Science+Business Media New York
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O’Raifeartaigh, L. (1993). Spin-Statistics and Topology. In: Gruber, B. (eds) Symmetries in Science VI. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1219-0_48
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DOI: https://doi.org/10.1007/978-1-4899-1219-0_48
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