Spin-Coherent States

  • Monique Combescure
  • Didier Robert
Part of the Theoretical and Mathematical Physics book series (TMP)


In this chapter we consider that the unit sphere \(\mathbb {S}^{2}\) of the Euclidean space ℝ3 with its canonical symplectic structure is a phase space. Then coherent states are labeled by points on \(\mathbb {S}^{2}\) and allow us to build a quantization of the two sphere \(\mathbb {S}^{2}\). They are defined in each finite-dimensional space of an irreducible unitary representation of the symmetry group SO(3) (or its covering SU(2)) of \(\mathbb {S}^{2}\) and give a semi-classical interpretation for the spin.

As an application we state the Berezin–Lieb inequalities and compute the thermodynamic limit for large spin systems.


Irreducible Representation Coherent State Geometric Phase Stereographic Projection South Pole 
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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Monique Combescure
    • 1
  • Didier Robert
    • 2
  1. 1.Batiment Paul DiracIPNLVilleurbanneFrance
  2. 2.Laboratoire Jean-Leray Departement de MathematiquesNantes UniversityNantes Cedex 03France

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