Abstract
A new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group) is presented. Some applications of the construction in quantum‐optics problems are discussed. The notion of phase space of a Lie group is studied. The possibility of describing the quadrature components of a photon, in view of the Lie group phase space, is pointed out. Examples of two‐ and three‐dimensional Lie groups including Heisenberg–Weyl group are considered.
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Guerrero, J., Man'ko, V.I., Marmo, G. et al. Geometrical Aspects of Lie Group Representations and Their Optical Applications. Journal of Russian Laser Research 23, 49–80 (2002). https://doi.org/10.1023/A:1014283531421
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DOI: https://doi.org/10.1023/A:1014283531421