# Configurations of points

@article{Atiyah2001ConfigurationsOP, title={Configurations of points}, author={Michael Francis Atiyah}, journal={Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}, year={2001}, volume={359}, pages={1375 - 1387} }

Berry & Robbins, in their discussion of the spin–statistics theorem in quantum mechanics, were led to ask the following question. Can one construct a continuous map from the configuration space of n distinct particles in 3–space to the flag manifold of the unitary group U(n)? I shall discuss this problem and various generalizations of it. In particular, there is a version in which U(n) is replaced by an arbitrary compact Lie group. It turns out that this can be treated using Nahm's equations… Expand

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To an ordered N-tuple (x1, . . . , xN ) of distinct points in the three-dimensional Euclidean space Atiyah has associated an ordered N-tuple of complex homogeneous polynomials (p1, . . . , pN ) in… Expand

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The geometry of point particles

- Physics
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2002

There is a very natural map from the configuration space of n distinct points in Euclidean 3–space into the flag manifold U(n)/U(1)n, which is compatible with the action of the symmetric group. The… Expand

Indistinguishability for quantum particles: spin, statistics and the geometric phase

- Physics
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The quantum mechanics of two identical particles with spin S in three dimensions is reformulated by employing not the usual fixed spin basis but a transported spin basis that exchanges the spins… Expand