Explain, following Ref. [1], the configuration space of identical
particles, and show that in 3 and higher space-dimensions, there
are only bosons and fermions, while in dimension 2 also "anyons"
can arise.
Describe the structure of the braid group (the homotopy group of
the configuration space in 2 dimensions) [2, Chapter 2].
Discuss as an example anyons that arise from fractionally charged
particles in the presence of a magnetic flux tube ([2, Chapter 4] and
[3]). Anaylse the system of two anyons in a harmonic well [3].
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[1] J.M. Leinaas and J. Myrheim, On the theory of identical particles,
Nuovo Cimento B37, 1 (1977).
[2] A. Lerda, Anyons, Lecture Notes in Physics, Springer (1992)
[3] F. Wilczek, Quantum mechanics of fractional-spin particles,
Phys. Rev. Lett. 49, 957 (1982).
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