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Canonical group quantization, rotation generators, and quantum indistinguishability

Authors: C.L. Benavides-Riveros, and A.F. Reyes-Lega

Ref.: in "Geometric and Topological Methods for Quantum Field Theory", edited by H. Ocampo, E. Pariguan, and S. Paycha, chapter 9 (Cambridge University Press, Cambridge), 344-367 (2010)

Abstract: Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum operators are the quantum version of Poincaré’s vector, i.e., the physically correct angular momentum operators for an electron coupled to the field of a magnetic monopole. In the second case, the obtained operators represent the angular momentum operators of a system of two indistinguishable spin zero quantum particles in three spatial dimensions. We explicitly show how our formalism relates to the one developed by Berry and Robbins. The relevance of the proposed formalism for an advance in our understanding of the spin-statistics connection in non-relativistic quantum mechanics is discussed.

Citations: 1 (Google scholar)

DOI: https://doi.org/10.1017/CBO9780511712135.010

Bibtex:

@incollection{Benavides_2010,
	doi = {10.1017/cbo9780511712135.010},
	url = {https://doi.org/10.1017%2Fcbo9780511712135.010},
	year = 2010,
	month = {apr},
	publisher = {Cambridge University Press},
	pages = {344--367},
	author = {Carlos Benavides and Andr{\'{e}}s Reyes-Lega},
	title = {Canonical group quantization, rotation generators, and quantum indistinguishability},
	booktitle = {Geometric and Topological Methods for Quantum Field Theory}
}